This was a very even, end-to-end game that was only decided in United's favour after Aberdeen went down to ten men in the middle of the second half.
The Tangerines had started the better and had an early penalty claim waved aside.
It took Aberdeen 15 minutes to create their first chance with ex-United man Lee Miller heading straight into the arms of Derek Stillie.
The keeper subsequently foiled a further two efforts from the striker and breathed a sigh of relief in the 27th minute when Gary Dempsey's curling 25-yard free-kick came down off the underside of the bar.
With a more attacking formation after the break, the Dons grabbed the lead in the 56th minute when another Dempsey free-kick was hammered home at the far post by Scott Severin.
But the Aberdeen lead was wiped out five minutes later when Barry Robson's curling free-kick was nodded in by Collin Samuel from eight yards.
The dismissal of Michael Hart, who had been sick on the journey down to Tannadice, in the 66th minute changed the game.
However it was not until the referee gave a dubious penalty decision that United finally took the lead.
Jamie Langfield was adjudged to have brought down David Robertson in the box, and Robson gleefully finished from the penalty spot.
Samuel wrapped it up in the final minutes with a killer third on the break as Aberdeen threw men forward looking for the equaliser.