The defeat leaves last season's Scottish Cup winners stuck in 10th place, seven points from the upper half of the SPL.
Terry Butcher's team, however, were able to regain second spot in the standings as they recorded just their second win in eight games.
The home side were undone by a Gary Warren double which came either side of Billy McKay's 22nd strike of the season.
Yet Hearts had twice equalised through Jason Holt and a deflected Andy Webster strike - but both times handed the initiative back to their Highland visitors within minutes.
The final whistle brought another round of boos from the maroon contingent amongst the 11,325-strong Gorgie crowd just a week after their team was dumped by Kilmarnock.
Ross County stretched their unbeaten run in 2013 to eight games with a 3-0 win against Motherwell at Global Energy Stadium.
After a slow start County went on to dominate the match with Ivan Sproule scoring his firth goal in as many starts to give County the lead in the 11 minutes from the break.
Second half goals from Richard Brittain and Iain Vigurs completed a fine second-half display from the home side.
Aberdeen were unable to make their chances count as Kilmarnock battled back to earn a 1-1 draw at Rugby Park.
Rory Fallon's brilliant volley gave the Pittodrie side the lead they deserved before Paul Heffernan got Kilmarnock back on terms five minutes before half-time.
After passing up a number of chances in the opening 45 minutes the second half brought more chances for the visitors. However, an inspired performance from Cammy Bell in the Killie goal ensured the game ended in a stalemate.
Rowan Vine's scrambled goal consolidated St Johnstone's position in the top half of the Premier League with a 1-0 win and delivered a major blow to St Mirren's chances of joining them.
Vine shot home from close range early in the second half after Murray Davidson had bundled the ball goalwards following Mehdi Abeid's corner in a goal that followed a similarly scrappy first 45 minutes on a bumpy McDiarmid Park pitch.
The home side built on the goal and hit the frame of the goal three times with home goalkeeper Alan Mannus not seriously troubled in the second half.
They moved into fourth place, level on 40 points with Motherwell, while St Mirren are now eight points adrift of the top six with six games left until the split.
- Sports & Recreation