The home side created by far the better openings but failed to kill the game off.
The visitors paid the penalty for a lack of punch up front with Christian Nade all to often isolated in the frontline.
While the game had no malicious tackles, the visiting side's lack of discipline saw them lose Marius Zaliukas on 73 minutes for a needless elbow aimed at Andrew Considine.
The bad feeling continued after the final whistle with Lee Wallace also getting a red card from referee Iain Brines for having too much to say for himself.
Aberdeen had a setback as early as the third minute when Charlie Mulgrew had to be replaced when he took a nasty knock in a challenge from Nade and had to be replaced by Considine.
Aberdeen ought to have taken the lead on nine minutes when Darren Mackie raced onto a clever through ball from Jeffrey de Visscher but, as the striker advanced into the area, Janos Balogh raced from his line to block his low right-foot effort.
Great interplay on 14 minutes between Lee Miller and Mackie saw the latter skip away from Zaliukas before driving in a shot from 16 yards which Balogh held comfortably.
Aberdeen stunned the visitors on 36 minutes with a fabulous opening goal.
From a free-kick rehearsed on the training ground, Scott Severin picked out Miller whose effort from ten yards bulleted into the left-hand corner of the net.
With 58 minutes gone, Sone Aluko skipped away from Robbie Neilson before flashing in a great near post cross which only required a touch from Miller to extend the home side's advantage.
At the other end minutes later, Andrew Driver drove past Richard Foster to play the ball into the area where a headed clearance from Alexander Diamond was taken first time by Nade but his effort was well off-target.
Miller should have added a second goal on 67 minutes when he latched onto a long Severin clearance.
The striker steadied himself, cutting inside Zaliukas, before driving in a stinging shot from 16 yards which Balogh did brilliantly to parry away at the expense of a fruitless corner.
On 73 minutes there was much drama from a Hearts corner kick. Zaliukas aimed an elbow at Considine and rightly received a straight red card for his stupidity.
A snapshot from de Visscher on 78 minutes deflected into the path of Diamond whose close-range effort went just past the upright.
Aberdeen had loud appeals for a penalty kick turned down in the 83rd minute as Mackie raced onto a de Visscher flick only for Wallace to make a desperate late but well-timed tackle.