The visitors' cause wasn't helped by two red cards during the second period for Barry Robson and Lee Wilkie.
The Dons forced two early corner kicks in a positive start to the match.
From the first of these a snap-shot from Jeffrey de Visscher ricocheted off Jordan Robertson and flew just wide of the upright with Grzegorz Szamotulski stranded.
On eight minutes a hooked left-foot shot from inside the area from Wilkie saw Jamie Langfield scrambling across his goal to fingertip the effort around the post.
The home side should have opened the scoring on 22 minutes when a lightning quick break started by Sone Aluko ended with his own 16-yard shot flashing off target.
Aberdeen had a major let-off on 34 minutes when Langfield again did brilliantly to turn a Wilkie header around the post.
On 39 minutes some excellent attacking play involving Aluko and Chris Maguire saw the latter's driven cross fall on to the head of Derek Young, but he got his effort all wrong and from six yards his header was well wide of target.
Aberdeen had their tails up at this stage and minutes later the visiting keeper Szamotulski pulled off a remarkable save to parry a Lee Mair header away to safety following an excellent Young cross.
Aberdeen finally made the deserved breakthrough in 45 minutes as Aluko timed his run to perfection to latch onto an intelligent Young through ball, before giving the keeper no chance with a stunning 18-yard drive.
After a sustained period of pressure early in the second half, Aberdeen almost grabbed the vital second goal.
Aluko picked out de Visscher whose powerful downward header from eight yards was brilliantly blocked by the visiting keeper.
On 64 minutes de Visscher produced a brilliant piece of individual brilliance when he beat three United defenders before crashing a tremendous shot off the crossbar.
With 67 minutes played Christian Kalvenes' long ball from left to right found Noel Hunt who skipped past several defenders before firing in a rising 20-yard effort which flew just over the bar.
The red mist descended on Robson on 77 minutes when his disgraceful two-footed challenge on McGuire left referee Kenny Clark no alternative but to send off the United skipper.
The afternoon got even worse for the visitors on 87 minutes. Lee Wilkie who had earlier been booked, earned himself a silly second yellow card for persistent fouling and was sent off.
The game was all over as a contest in 89 minutes when Lee Miller contested a high ball with Darren Dods and the ball broke kindly for the big striker to lash home a shot.