The Dons striker bagged his seventh goal of the season when he volleyed home Scott Severin's free-kick. It set up a fifth successive home victory.
Marius Zaliukas saw red in a fiery second half for elbowing Andrew Considine when a melee broke out in the Aberdeen penalty box in the build-up to a Hearts corner. It later emerged Hearts defender Lee Wallace was also sent off after the final whistle.
Aberdeen made one change to the side that defeated Inverness 3-0 with the versatile Richard Foster starting ahead of Lee Mair who dropped to the bench.
Hearts also made one alteration to their starting 11 with Michael Stewart replacing the injured Bruno Aguiar.
The home side were forced to make an early substitution with Andrew Considine coming on after four minutes for Charlie Mulgrew who hobbled off following a challenge with Frenchman Christian Nade only 15 seconds after kick-off.
Hearts started the more lively of the two teams in front of a packed Pittodrie crowd but had little to show for their early dominance apart from a weak Andy Driver header that was easily gathered by Jamie Langfield.
However it was the home side that should have taken the lead after 10 minutes when Jeffrey De Visscher played in Darren Mackie but the pacy striker shot straight at Janos Balogh in the Hearts goal.
Mackie did better moments later when he dribbled past two defenders before unleashing a low, curling shot that Balogh did well to save.
Hearts skipper Christophe Berra picked up the first booking of the day for a late tackle on Lee Miller after 24 minutes.
Jimmy Calderwood's side were continuing to press for the opener with De Visscher volleying wide of the Hearts goal from the edge of the box before Gary McDonald stung the palms of Balogh soon after.
The Dons did take the lead after 36 minutes with a well-worked free-kick. Scott Severin flighted the ball from just inside the Hearts half to the back post to Miller who had managed to evade his marker Berra and clinically despatched the ball on the volley past Balogh.
Mackie and Marius Zaliukas joined Berra in referee Iain Brine's notebook as the half drew to a close.
Hearts enjoyed a healthy amount of possession after the restart but struggled to create anything from their dominance, although Driver did flash an effort over the bar from an acute angle after 55 minutes.
Sone Aluko, who had barely touched the ball in the first half, suddenly came to life and threaded a beautiful cross into the Hearts box but Miller and De Visscher were both unable to connect with the goal gaping.
Miller almost grabbed his second after 69 minutes when he raced on to a Severin pass before cutting inside past Zaliukas but his powerful shot was pushed clear by Balogh.
The talking point of the match occurred after 73 minutes. While Michael Stewart was waiting to take a corner for Hearts a huge melee broke out in the penalty box after Zaliukas appeared to elbow Considine. The Lithuanian was given his marching orders while Miller and Nade were booked for their parts in the altercation.
Csaba Laszlo made his first changes soon after with Gary Glen and Eggert Jonsson coming on for Nade and Laryea Kingston.
Considine joined them in the book for a crude challenge on Driver minutes later as the game became increasingly ill-tempered.
With less than 10 minutes to go the home support were appealing for a penalty when Mackie fell in the Hearts box under pressure from Wallace but referee Brines waved away the appeals and booked Severin for his protests.
The tiring Sone Aluko was replaced by Chris Maguire minutes before the end and Lee Mair came on for McDonald as Calderwood's side held on to end 2008 with three points.
Robbie Neilson and Chris Maguire appeared to have been booked after the final whistle amidst more angry scenes but it was the home support who left happy.
It later emerged Hearts defender Wallace had also been sent off after the final whistle.