The Scotland midfielder's 54th-minute penalty, after Russell Anderson handled the ball on the goal-line, was enough to settle an untidy encounter.
Aberdeen were reduced to 10 men 11 minutes from time when Scott Severin was given a straight red card for a foul on Bruno Aguiar on the halfway line.
Hearts made a breathtaking start as they sought to blow Aberdeen away and Deividas Cesnauskis was just a yard wide with a 10-yard shot after Roman Bednar had cut the ball back.
Edgaras Jankauskas was next to try his luck - from 25 yards - but the ball was always going too high.
For all their possession in the early stages, Hearts seldom seriously threatened Jamie Langfield and the Dons goalkeeper was well protected by his defence.
Aberdeen came more and more into things and Barry Nicholson hooked a shot wide, although Craig Gordon looked unconcerned.
Steve Crawford then ruffled the side-netting but the angle was always against him and Hearts breathed easy.
It was not until the final minute of the first half that there was a shot on target from either side, when Langfield did well to smother a 20-yard drive from Bednar which came through a crowd of players.
The hosts had the better of the second half and took their reward with the crucial goal from Hartley nine minutes after the break.
Hearts had chances to add to their lead and Langfield produced the save of the match to deny Cesnauskis.
But one goal was to prove sufficient to send the Hearts fans home happy.