With United struggling all season and near the bottom of the SPL, few, if any, would have thought that the Terrors would totally outplay their opponents and win by a margin which should have been considerably wider. But this was one of those games.
After a scrappy opening four minutes, Barry Robson gave the Tangerines support some encouragement with a weaving run and 20-yard shot that Dons keeper Ryan Esson did well to hold.
Lifted by their good start, United continued to press and it came as no surprise when they finally took the lead in the 19th minute.
Russell Anderson crudely fouled Jason Scotland to earn himself a caution and, from Robson's free-kick, Stevie Crawford's shot was blocked on the line by Noel Whelan. The rebound fell to Alan Archibald who subsequently volleyed the ball into the net from six yards.
The Tangerines doubled their lead ten minutes later. After fabulous wing work, Mark Wilson sent over an inviting curling cross which Robson headed on to the underside of the bar. The ball bounced down for James Grady to gratefully tap in from two yards.
But Wilson was the villain four minutes later when he allowed Richie Byrne to beat him to the ball and head in at the far post, diving to meet Jamie Winters' free-kick.
Despite the setback, United ploughed on and regained their two-goal advantage four minutes before the break. Grant Brebner's chip was wonderfully controlled by Scotland who slipped the ball through to Crawford. The striker showed all his international class to coolly tuck the ball under the diving keeper.
After Aberdeen's poor first-half display, the question was how would they come back in the second half but it went from bad to worse for the Dons when United killed the game with a brilliant goal by Grady.
Following some excellent passing between Scotland and Crawford, the latter fired the ball towards Grady who teed it up, and volleyed the ball into the far corner from 14 yards.
With Aberdeen deflated, United, playing with freshly injected confidence, pulled them apart. It should have been five on the hour when Scotland set the ball up for Robson but Esson pulled off a super stop.
And the keeper repeated the feat in the 72nd minute when he pulled off another great save from Robson's fierce shot and he denied the midfielder again with three minutes left.
But despite missing a host of chances, the Tangerines left the field to a standing ovation as they progressed to the semi-finals.