Haber becomes Paul Hartley's 14th signing this summer with the Bairns boss delighted with his recent arrival.
"I'm absolutely delighted to recruit a player of Marcus' calibre," said Hartley.
"I am surprised that a player of his quality has become available, but equally pleased to have signed him.
"He will add great experience and presence to our front line and I'm sure will contribute goals too. Ww identified the need to strengthen our frontline and I feel the signing of Marcus does just that."
Marcus Haber played 41 times for Dundee, scoring 10 goals.
Dundee made only one change from Friday night's game in Aberdeen. Kosta Gazdhalov came in for Darren O'Dea who was not registered in time for the original date. Falkirk made three changes, David McCracken for Peter Grant, Blair Alston for Connor McGrandles and Tom Taiwo for Lee Miller.
Dundee started promisingly with Nick Ross sending Nicky Low to the byline in the first minute, but there were no takers for a dangerous cross. The Bairns, however, settled quickly and took the game to the Dee. Falkirk tried to play their way through the Dundee midfield and defence with neat passing, and were sometimes allowed rather too much room to do so.
With less of the ball Dundee looked more dangerous. Kane Hemmings and Greg Stewart managed to find a surprising amount of space, and Hemmings was often on the shoulders of the last defender, trying to burst clear.
Twice in quick succession Dundee passed their way through the Bairns' defence. Delightful play between Gary Harkins and Greg Stewart almost played Hemmings in, but Danny Rogers managed to dive on the ball. Ross then blazed his shot over the bar from a tight angle after Harkins' had cleverly created the opportunity. For all Falkirk's good football they weren't convincing when they reached the penalty area. Blair Alston did force a good save from Scott Bain with a shot from 18 yards.
The home fans had been getting frustrated with a series of narrow offside decisions that went against Dundee. When they did beat the offside trap after 38 minutes they took the lead. HEMMINGS took a long pass from Paul McGowan and from 18 yards crashed his shot into the net off the underside of the crossbar.
The Bairns hit back almost immediately with a goal that owed nothing to the neat football they'd been playing. Dundee's attempted breakout from a corner broke down and Mark Kerr sent the ball straight back into the home penalty area. The unmarked John Baird was onside and he played the ball across for Paul WATSON to force in the equaliser.
The Dark Blues recovered well from that disappointment and went on to take charge of the match in the second half. It took a while for the Dee to click as a series of promising moves didn't quite come off. There was almost a scare when Craig Sibbald's run took him deep into the penalty area, but he waited far too long before shooting and lost the chance. It was just about the only time in the second half that the Bairns looked truly dangerous. Their failure to take advantage cost them dearly as the Dee went back in front shortly afterwards with a marvellous goal.
Paul McGowan found Paul McGinn on the right. The full back took a great first touch to knock the ball into space and fired over a fine cross that eluded Harkins only for HEMMINGS to smash home an unstoppable far post volley from six yards - his ninth goal in the last six games.
With Dundee in the lead the Bairns pushed forward and looked increasingly vulnerable against Dundee's skillful attackers. Paul Hartley added to Falkirk's problems by sending on Rory Loy to replace Nicky Low with 20 minutes to go. It looked a bold move and it quickly paid off with an excellent third goal.
Hemmings broke down the right with Loy in support. The Falkirk defence were all watching the ex Bairn and failed to spot Harkins' run through the middle. Hemmings timed his pass perfectly, and HARKINS took a touch before drilling a low shot into the corner of the goal from 18 yards.
Julen Etxabeguren was a welcome sight for the home support, returning from his eye injury a few minutes from full time when Kosta Gadzhalov was suffering from cramp.
Greg Stewart nearly put the Dee out of sight when he dribbled into the penalty area and shot against the outside of the post. Falkirk worked hard to try and get back into the match, but failed to create any chances except for a stinging 20 yarder in injury time from Will Vaulks that Bain did well to turn away.
Dundee now move on to Dumbarton for the 5th round against another Championship side. Tonight the Dark Blues showed that when their attackers are on form they can make life very difficult for teams from outside the Premiership. Falkirk are one of the best sides in the Championship, and they showed tonight why they are widely admired for the quality and style of their football. However, they had no answer to Dundee's attacking flair, and that was the crucial difference that gave the Dee a deserved win.
Dundee FC 4-4-1-1
McGinn, Gadazhalov (Etxabeguren 70), Konrad, Holt
Stewart, McGowan, Ross, Low (Loy 70)
Unused subs: Mitchell (gk), Irvine, Curran, Kerr, Wighton
Goal: Hemmings (38, 59), Harkins (73)
Falkirk FC 4-4-1-1
Vaulks, Watson, McCracken, Leahy
Alston, Muirhead, Kerr, Taiwo (McHugh 66)
Unused subs: Tokarczyk (gk), Smith, Cooper, O'Hara, Gallagher, Maybury
Goals: Watson (40)
Booked: Watson (foul on Hemmings)
Referee: Willie Collum. Assistants: Alastair Mather, Alasdair Ross. 4th official: Colin Steven.
Report: James Christie
The only change from Tuesday night's winning team was that Craig Beattie replaced Nicky Riley, with Martin Boyle moving to the right wing.
Dundee started well against an uncertain Bairns' defence, that was leaving space in front of the full backs and consistently failed to clear the ball when they had the chance.
The Dark Blues had the first chance after 10 minutes when Peter MacDonald's header from a corner was hacked off the line by Millar. The Dee continued to threaten but the vital goal fell to Falkirk after 18 minutes. Millar's inswinger was headed home at the near post by Mark BECK.
Falkirk were not playing the fluent passing game that has caused Dundee so many problems this season, but they posed a different threat today in the lanky form of Beck, on loan from Carlisle. He might not have been particularly elegant on the ground, but in the air he unsettled the Dundee defence.
Craig Beattie nearly fashioned a quick equaliser. He turned Kingsley brilliantly to run clear, but keeper McGovern managed to block his shot.
Falkirk's next corner nearly led to a goal, but for Dundee. Declan Gallagher won the ball superbly to send Boyle racing down the right. With the Bairns' defenders backtracking he ran on and rolled the ball across for Beattie 14 yards out. The striker should have scored, but went for power rather than accuracy and hit the ball straight at McGovern.
The Dee had a rather fortunate escape themselves when Loy's run set up a scramble in which Grandles and Beck had shots charged down.
The Falkirk defence continued to look vulnerable, but Dundee couldn't force the equaliser. A third golden chance fell to Craig Beattie. MacDonald chested Davidson's cross down, but from eight yards Beattie smashed his shot against the outside of the post.
The Dark Blues defence may have looked more secure than the Bairns', but it was hardly convincing and Dundee had a final let off when Loy's 18 yard shot took a deflection and flew narrowly wide.
Sadly for Dundee they couldn't carve open the Bairns' defence as easily in the second half and they paid the price for squandering their first half chances. Falkirk looked more comfortable sitting back, and their midfield finally started to offer their defence some protection.
Boyle was still lively on the right, and a good run ended with a very poor late challenge by Millar that the officials somehow missed.
Jim McAlister took a head knock bravely challenging for an Irvine cross. Ryan Conroy took his place on the left of midfield. Dundee were exerting plenty of pressure, but there was little composure or conviction and it was the visitors who came closest to scoring again.
Davidson dived into a challenge on Millar who was heading for the byline. He took both man and ball. Referee Mr McKendrick decided it was more man than ball and pointed to the penalty spot. Last week Kyle Letheren saved a spot kick by standing his ground. Today he saved Millar's penalty with a magnificent low save to his left.
This gave the crowd a huge lift and they got right behind the Dee. Christian Nadé came on for Beattie, and then Nicky Riley replaced Rae. Dundee now had three strikers and two wide players, but they lacked a midfield to control the game.
Dundee's desperate attempts to chase an equaliser always left them vulnerable to a Falkirk break. Beck was largely ineffective in the second half, but Rory Loy's probing runs were far more dangerous. His team mates didn't get forward to support him, however, as the Bairns concentrated on watching the clock.
Falkirk's time wasting was largely tolerated by the referee. Mr McKendrick was infuriating the home crowd with some unnecessary fussiness, but Dundee's problems were of their own making and the Dee could have no complaints over the big decisions by the referee today.
Dundee did manage to force the ball into the net in injury time when Gallagher bundled Irvine's cross into the net along with the keeper. Such goals have been allowed recently, but no-one was very surprised when Mr McKendrick refused to allow it.
All Dundee had to show for their second half pressure were some wayward shots from distance and a couple of Boyle shots that were charged down or deflected. All the other attacks petered out with poor final balls and poor choices.
In recent games Dundee have been tight at the back and have taken the few chances that came their way. Today they conceded a disappointingly soft goal then spurned some excellent chances. In the first half they actually played far better than in many recent wins. Without scoring that counts for nothing, and the way that Dundee fell away in the second half disappointed everyone.
The hectic spell of five games in 15 days is now over, with the Dee having taken 10 points but lost the top spot. They now have a week to regroup and prepare for the big showdown at New Douglas Park next week. The Dark Blues will need all the support they can get in what is surely their biggest game for several years.
Dundee FC 4-4-2
Irvine, Gallagher, Cummins, Dyer
Boyle, Davidson, Rae (Riley 72), McAlister (Conroy 55)
Beattie (Nadé 64), MacDonald
Unused subs: Twardzik (gk), Kerr, McBride, Doris
Booked: Irvine (foul on Kingsley)
Falkirk FC 4-4-2
Vaulks, McCracken, Kingsley, Chalmers
Alston (Leahy 64), Millar, Sibbald, McGrandles (Durojaiye 86)
Beck, Loy (Flynn 89)
Unused subs: Bowman (gk), Small, Hogg, Shepherd
Goal: Beck (18)
Referee: John McKendrick
Report: James Christie
Following the disappointing performance against Livingston John Brown made five changes. New signings Christian Nadé and Stephen Hughes came into the starting line-up along with Kyle Benedictus, Willie Dyer and Iain Davidson. Only Jim McAlister kept his place from the midfield and attack against Livi, with McBride, Rae, Conroy, Boyle and Wighton dropping onto the bench.
Gallagher and Benedictus were at centre back, with Lockwood the free man behind them. Irvine and Dyer played as wing backs, with a central midfield of Hughes, Davidson and McAlister.
Reverting to the 3-5-2 formation that Dundee tried early in the season was a disappointing failure. In the 30 minutes till the Dark Blues switched to the usual 4-4-2 they were wide open down the flanks and offered no threat up front.
The early signs were ominous. Duffie made space on the right and Letheren did well to save Alston's close range volley. On the other wing McGrandles' burst clear. His deflected cross was parried by Letheren and Dyer blocked Loy's follow up.
It was no surprise when Dundee's vulnerability at the back cost them a goal. After 16 minutes Benedictus slipped, allowing Roberts to run clear down the right. McGRANDLES took his cross and crashed the opening goal in off the post from 12 yards.
The Bairns were comfortably in control and should have made it 2-0 when Millar played a neat exchange with Loy, but with the goal gaping he placed his shot too close to Letheren, who turned it wide for a corner.
Dundee now switched to 4-4-2, with Lockwood moving to left back and Dyer to left midfield. Irvine dropped back to play as an orthodox right back and Hughes moved to right midfield.
The changes made Dundee more secure at the back, but they were still utterly toothless in attack. MacDonald and Nadé received dreadful service from a midfield that could neither worry the Falkirk defence nor protect the Dark Blues' own rearguard.
The Dark Blues' hopes rested on reaching the half time interval only a goal in arrears, with the chance to reorganise for the second half. Sadly things got even worse in the last minute of the first half.
Kyle Benedictus slipped again, allowing Loy to run clear. He took the ball round Letheren, who brought him down. Referee Mr Madden produced his red card and the Dark Blues' slender hopes of getting anything from the match vanished.
Christian Nadé was the unfortunate player to be sacrificed to allow substitute keeper Dan Twardzik to take his place in goal. It wasn't a happy debut for Nadé who'd had no opportunity to show what he could do in a poor team display.
Twardzik gave the Dark Blues support something to cheer at last by diving left to block Loy's weak penalty, but that was the last moment the fans had any cause to smile.
Gavin Rae came on at half time, replacing Stephen Hughes, and Jim McAlister moved to right midfield.
Falkirk should have extended their lead within 20 seconds of the restart. Benedictus misjudged a bouncing ball, and Roberts ran in on goal. He seemed sure to score, but carelessly dragged his shot wide.
The half time change made little difference to the Dark Blues. McAlister perked up the right side of the team, but Dundee missed his drive in the middle.
Peter MacDonald worked tirelessly chasing optimistic long balls, but he was denied any effective support and could do nothing on on his own.
Falkirk were in cruise control and embarrassingly comfortable at this stage. Twardzik was kept busy with a succession of shots from distance and around the edge of the penalty area. The only criticism that could be made of Falkirk was that they showed a certain carelessness in the final third, and were content to take pot shots rather than drive through the Dundee defence.
Roberts did pass up a golden close range chance when he wastefully flicked a cross well wide. However, he made amends when he raced down the left and whipped a dangerous low cross into the goal mouth. LOY timed his run perfectly and couldn't miss from three yards; 2-0 and the game was over.
Peter MacDonald sent a free kick wide from 20 yards. He then played substitute Martin Boyle in to shoot from an angle, but McGovern spread himelf well to save. Apart from those efforts Dundee could point only to a Gallagher header that drifted wide following a corner and a couple of wild shots from MacDonald and Irvine.
The Bairns saw out the match easily, content to settle for a two goal win rather than punishing the Dark Blues more severely. Dundee played poorly and lost badly at Falkirk in September. If anything this was a worse performance today. In the previous match Dundee created good early chances. Today Dundee didn't even have a shot, or an attack worth reporting till the game was out of reach.
There was a very healthy turn out of 913 Dundee supporters in today's crowd. Every single one of them must have felt let down by this performance. Sadly Dundee got just about everything wrong today and Falkirk were superior in every respect.
Falkirk FC 4-4-2
Duffie, Flynn, Vaulks, Kingsley
Alston (Fulton 80), Millar, Sibbald (Leahy 85), McGrandles
Roberts (Shepherd 89), Loy
Unused substitutes: Bowman (gk), Durojaieye, Dick, Small
Goals: McGrandles (16), Loy (72)
Dundee FC 3-5-2 for first half hour, then 4-4-2
Gallagher, Lockwood (Boyle 80), Benedictus
Irvine, Hughes (Rae 45), Davidson, McAlister, Dyer
Nadé (Twardzik gk 44), MacDonald
Unused subs: McBride, Conroy, Monti, Wighton
Bookings: Lockwood (foul on Alston), Benedictus (foul on Roberts), Davidson (pushing the Falkirk defensive wall)
Sent off: Letheren (denying goal scoring opportunity)
Attendance: 4,183 (913 Dundee supporters)
Referee: Bobby Madden
Report: James Christie