Hearts ended a run of three straight defeats as Dundee's relegation fears deepened with a sixth straight loss.
Isma Goncalves raced onto Don Cowie's pass and fired home from a tight angle via a deflection off Darren O'Dea.
The hosts might have been further ahead by half-time but Arnaud Djoum's header was superbly saved by Scott Bain.
Dundee offered little but Jack Hamilton was forced to tip Tom Hateley's free-kick onto a post and Craig Wighton dragged a golden chance wide.
But it was far too little from Paul Hartley's side, who remain in ninth place, only a point above the relegation play-off spot.
Smith, Buaben, Nowak, Struna
Kitchen (c), Tziolis
Cowie, Djoum (Martin 60), Walker (Currie 64)
Goncalves (Johnsen 89)
Unused subs: Noring (gk), Avlonitis, Choulay, Beith.
Goals: Goncalves (13).
Dundee FC 3-5-2
Higgins, O’Dea (c), Holt
Hateley, O’Hara, Vincent, McGowan, Kerr
Ojamaa (Wighton 58), Haber
Unused subs: Mitchell (gk), Ross, Dryden, Ian Smith, Kevin Gomis.
Booked: Kerr (foul on Smith).
Attendance: 16,304 (605 Dees).
Referee: Crawford Allan. Assistants: Gordon Crawford, Ralph Gordon. Fourth official: Don Robertson.