The hosts took the lead after only three minutes at Tannadice on Saturday through captain Jon Daly before Dons goalkeeper Mark Howard punched the ball into his own net three minutes later.
David Goodwillie looked to have put the game beyond the Dons when he slotted home from the penalty spot after Paul Hartley had fouled Craig Conway in the box with only nine minutes on the clock.
However, Scott Vernon pulled a goal back with a magnificent volley after 26 minutes to give his side some hope for the second half.
Aberdeen boss Mark McGhee was sent to the stand just before the break for his over-zealous protests after his side were denied a penalty when Zander Diamond looked to have been held in the box by Garry Kenneth.
After surviving an early scare when Chris Maguire was denied by an instinctive stop by Dusan Pernis in the opening 60 seconds, it was United who broke the deadlock after less than three minutes of play when David Goodwillie's blocked shot rolled kindly into the path of Irishman Daly who scored from six yards out. And the Tangerines doubled their lead after six minutes when Mark Howard, from an inswinging Conway corner, haplessly punched the ball into his own net - much to the frustration of the Dons supporters who had travelled down the A90 to cheer on their team in impressive numbers.
With the home side reeling, United had the chance to add a third after only nine minutes when Hartley was adjudged to have tripped Conway in the box.
The Dons skipper received a booking for his angry protests at the decision and Goodwillie powered the ball past Howard.
United should have added a fourth when Daly, clean through on goal, weakly shot into the grateful hands of Howard before the Dons pulled a goal back after 26 minutes.
Following a Jerel Ifil cross into the penalty area, Vernon - the former Colchester striker - showed terrific skill to chest and volley the ball high past Pernis.
The Dons were denied a penalty six minutes before the break when Zander Diamond looked to have been held by Kenneth, with the frustrated Aberdeen manager McGhee sent to the stands for his protest.
There was still time before the whistle for Howard to tip Scott Severin's rasping 40-yard drive over the bar as an action-packed half came to a close.
Nikola Vujadinovic made his first appearance for the Dons after 50 minutes in place of the injured Ifil.
Goalkeeper Howard had to be alert to push a curling Conway free-kick over the crossbar in United's opening attack of the second half.
Aberdeen made a double change after 62 minutes with Darren Mackie and Josh Magennis replacing the tiring Peter Pawlett and Mitchel Megginson as they searched for the goal that would get them back into the match.
However, it was United who looked the more likely to add another with full-back Barry Douglas going close from a set-piece and David Robertson blazing over from 10 yards.
United's Slovakian stopper Pernis produced a superb save to keep out Hartley's powerful free-kick after 78 minutes.
The hosts finished the game strongly with the lively Goodwillie going close on a couple of occasions.
The Dons produced a better display in the second half but were made to pay for their terrible start as they slumped to a second Scottish Premier League defeat in a row.