The strangely hesitant Dons never at any stage seemed to believe in themselves as they chased one of the European places for next season.
Aberdeen got off to a disastrous start when United scored within 30 seconds.
Morgaro Gomis' ball over the top saw Collin Samuel get behind Richard Foster, who conceded a penalty after clipping the striker's heels.
United striker Jon Daly made an immaculate job of converting the penalty kick.
Aberdeen's response was immediate as they forced a free kick 30 yards out. Scott Severin's fierce effort fell into the path of Steve Lovell who diverted the ball home past a stranded Derek Stillie.
The unbelievable start to the game continued after nine minutes when Foster was upended in the box by David McCracken as he drove straight at the heart of the defence.
Top-scorer Darren Mackie stepped forward to comfortably knock the ball home.
The goals kept coming when a Greg Cameron free-kick found Noel Hunt whose powerful header flew past Jamie Langfield on 13 minutes to bring the sides level again.
On 17 minutes Dundee United took the lead again when a poor defensive header by Dons skipper Russell Anderson fell to Cameron, who took one touch before smashing home a great shot from 16 yards.
Aberdeen almost forced an equaliser on 48 minutes when Mackie's clever chip almost reached Stillie at his far post.
United shocked their hosts minutes later when Gomis sent Hunt free and his cracking effort from 18 yards cannoned off the upright back into the path of Cameron, who gleefully slammed the ball into the unguarded net.