In a game of few chances it was the home side who ran out worthy winners, although this game was never a classic on a poor Pittodrie playing surface.
The home side made two changes to the team which narrowly won at Falkirk last week. Illness meant that Darren Mackie didn't make it, with Gary Dempsey dropping to the bench, fit again Craig Brewster and Jamie Smith were recalled to the starting 11.
Hearts were without Ibrahim Tall, who failed to recover from a groin injury, his place going to Tomas Kancelskis.
Following an untidy start to the match by both sides it was Aberdeen who grabbed the vital opener on eight minutes. Brewster sent the ball wide to Barry Nicholson, whose clever ball behind the Hearts defence found Steve Lovell racing to the edge of the area and he fairly hammered the ball home, giving Craig Gordon no chance.
On 15 minutes Michael Hart had to look lively to stop a Calum Elliot effort off his own line with the Velicka looking to pounce.
Diminutive midfielder Laryea Kingston worked a great shooting opportunity for himself on 33 minutes, but from 22 yards he blazed wildly over. At the other end, minutes later, a Smith free-kick was partially cleared to the edge of the area, where a fierce Nicholson drive looked goalbound until it struck Christophe Berra and deflected wide.
With the home side now very much in the ascendancy a Russell Anderson flick-on found its way to Brewster, whose volley on the turn was brilliantly palmed away by Gordon.
On 51 minutes, Hearts second-half sub Michael Pospisil linked up with Andrew Driver whose downward header was easily held by Jamie Langfield.
Aberdeen were awarded a free-kick on 55 minutes, which was played into the area by Scott Severin, the ball was headed into the path of Nicholson by Lovell, with the midfielder's effort from 15 yards, being well held by Gordon at the second attempt.
Hearts day wasn't getting any better when Kingston deservedly picked up a red card on 63 minutes for a reckless late challenge on Nicholson.
Aberdeen ought to have put the game beyond the visitors on 77 minutes. Richie Foster's clever ball into the path of Lovell saw the striker turn his marker before firing in a drive, which took a wicked deflection off Lee Wallace, before Berra headed the ball off the line with his keeper beaten.
Despite their supremacy Aberdeen had to survive a late scare when a header from Edgaras Jankauskas almost fell for Pospisil, but Langfield got down bravely at his feet to smother the ball at the second attempt.