Craig Levein's side capitalised as the Aberdeen defence crumbled after Lee Miller was sent off for a second bookable offence in the second half as the Terrors secured a 4-1 victory.
Dundee United started the match brightly with Mark De Vries, making a return to his former club Hearts' Tynecastle ground for the night, looking particularly dangerous.
Aberdeen were largely pinned back in their own half for the opening 15 minutes. They produced some good passages of play on the break but did nothing to trouble the United goalkeeper.
But against the run of play it was the Dons who took the lead as the United defence had their first wobble of the match as their opponents won a corner.
Barry Nicholson sent in the set-piece which was headed towards goal by Zander Diamond. Lucasz Zaluska in the Tangerines goal cleared the effort but his defenders failed to clear the ball from the area and Andrew Considine punished them as he blasted in a shot.
For a few minutes it looked as if Levein's side would crumble after having their confidence knocked, but they found themselves back on level terms after less than five minutes.
Darren Dods rose above the Aberdeen defence and sent an unstoppable header towards goal giving Jamie Langfield no chance of making the save.
Lee Wilkie, playing the captain's role following the departure to Celtic of talismanic skipper Barry Robson, missed a gilt-edged chance to give United the lead with about five minutes of the half remaining but his header went centimetres wide of the target.
Christian Kalvenes, playing his first game after a long injury lay-off, fired United in to the lead just before the hour mark as he headed in a Craig Conway corner.
Conway looked to have put the game out of reach on 65 minutes when he fired in from the edge of the area.
Any hopes that Aberdeen had of making a comeback went out of the window on 68 minutes when Miller was given his marching orders after picking up a second yellow card.
And things went from bad to worse for the Dons as a misunderstanding between Langfield and Scott Severin gave Morgaro Gomis the chance to race in and make it 4-1.