Steve Pressley played the captain's part to put Hearts within touching distance of a UEFA Cup place.
Pressley tucked away a 56th minute penalty to put the Edinburgh side ten points clear of fourth-placed Kilmarnock.
It was not the most fluent of performances but Hearts will not be concerned, as the three points were the priority.
In a poor first half, neither side looked capable of breaking the deadlock. Mark De Vries saw a 20-yard shot comfortably saved by Marco Ruitenbeek after he evaded marker Lee Bullen in the 17th minute but that was Hearts' only shot on target in the first half.
Dunfermline, who had played second fiddle to Hearts in the early part of the game, came more into it as the half wore on.
David Grondin swept an angled free-kick well over before Stevie Crawford had an opportunity only to see his ten-yard shot blocked by defender Andy Webster.
Webster gave the ball away in a dangerous position six minutes from the break but Barry Nicholson's final shot was wayward.
Nicholson had an even better chance on the stroke of half-time. With Hearts appealing for handball against Steve Hampshire, Craig Brewster picked out Nicholson but the midfielder's shot lacked power and Tepi Moilanen saved easily.
Hearts made the breakthrough eleven minutes into the second half when Bullen pulled down De Vries in the penalty area for a clear penalty.
Pressley sent Ruitenbeek the wrong way with the spot-kick and the goal rejuvenated Hearts.
Scott Severin had a chance to extend Hearts' lead shortly afterwards with Ruitenbeek off his line but he chipped the ball tamely into the goalkeeper's arms.
Dunfermline pressed for the equaliser but Hearts soaked up the pressure and Moilanen was never under serious pressure.
Hearts had the better chances to kill off the game but substitutes Andy Kirk and Kevin McKenna both saw late efforts expertly saved by Ruitenbeek.