Referee Charlie Richmond ruled that Scott Wilson had fouled Lee Miller in the area and Hartley made no mistake.
Ironically, it was Miller that was involved in Rangers' much-disputed award against Hearts in midweek.
Hearts skipper Steven Pressley was once again missing from the defence due to a virus and Paul Hartley took the captain's armband.
Hearts made a bright start and a great run from Deividas Cesnauskis split the home defence but his cross was just a yard too far in front of Dennis Wyness with Derek Stillie exposed.
But it was Dunfermline who took control after that. A slip by Christophe Berra gave Georgi Hristov an opportunity but the Hearts defender recovered to avert the danger.
It was a warning that went unheeded. Moments later, Simon Donnelly picked out Hristov with a clever pass and the Macedonian striker's shot was blocked by the legs of Craig Gordon.
Shortly afterwards, Lee Wallace misjudged a high ball in his area and it took another save from Gordon to keep out a Donnelly shot which was bound for the bottom corner.
Dunfermline had a strong penalty claim turned down by the referee when the ball appeared to strike the arm of Berra in his area.
But the home side broke the deadlock after 33 minutes. Ian Campbell's corner picked out Scott Wilson and his six-yard header had enough pace to beat Gordon.
The goal prompted a response from Hearts and a 25-yard shot from Lee Miller was tipped over the top by Stillie.
Cesnauskis waa the first player to be booked when referee Richmond ruled that he was guilty of making too much of a touchline challenge from Hristov.
Dunfermline were worth their half-time advantage and they came out in the second half with all guns blazing.
Substitute Derek Young just failed to connect with a Jesper Christiansen cross and then Gordon beat out a long-range shot from Darren Young.
Hearts had another escape when a back-post header from Andy Tod was just a foot too high.
Miller should have equalised after 56 minutes when Wilson lost his footing but the striker shot narrowly wide from 16 yards.
Hearts were awarded a penalty after an hour when Wilson was adjudged to have fouled Miller as both players went for a high ball and Hartley sent Stillie the wrong way with the spot-kick.
Dunfermline should have gone back in front when Gary Mason had a free header in front of goal but directed it straight at Gordon.
Jamie McAllister tested Stillie with a low shot which the goalkeeper failed to hold but the Dunfermline defence scrambled the ball clear.
Substitute Mark Burchill had a chance at the end but could not get a clean header on Wyness' cross.