The visitors stormed back from conceding an early goal to take advantage of some comical defending from United and take all three points from a game which was both entertaining and open.
The game was not short of action from the outset, with two goals in the first quarter of an hour.
United got off to a blistering start in the eighth minute with a wonderfully worked move that ended with a fantastic strike from Jason Scotland.
Derek McInnes started the move with a quickly taken free-kick out wide to Barry Robson. The midfielder returned the ball to his captain who slid it inside to Scotland and the striker turned on his heels before driving high into the top corner from eight yards.
However, the lead only lasted five minutes when the visitors equalised courtesy of a gift from the United defence.
Paul Ritchie mysteriously left an innocuous cross from the right believing his keeper would gather, only for Derek Riordan to take advantage of the mis-communication and hit the ball in from four yards.
Five minutes later, Garry O'Connor for the Hibees, followed by Grant Brebner for the Tangerines, both came close to grabbing the lead for their respective sides.
It was all action for the 10,152 crowd as Mark Kerr's 15th-minute volley was brilliantly parried to safety from Simon Brown.
The visitors who took the lead in the 23rd minute with a goal that looked suspiciously offside. A high ball was hit over the United defence to Alen Orman and as the referee looked to his assistant for a flag, the ball fell to O'Connor who thumped it in from ten yards.
To climax a superb half, Jim McIntyre struck the bar on the stroke of half-time, almost giving United a deserved equaliser as he caught a Robson cross from the edge of the box.
The Terrors began the second half with a flashing 55th minute header from McIntyre that flew inches wide, but they were close to losing another when Riordan and Craig Rocastle came very close.
Indeed, the visitors did extend their lead in the 58th minute through another ridiculous piece of defending from United.
Yet another tame cross appeared to be going nowhere until McIntyre popped up to head the ball past his own keeper into the path of Orman who had the easiest of tasks to tap the ball in from two yards.
United's pain was complete when Steven Whittaker took advantage of a clash between defenders Ritchie and Alan Archibald to set the ball up for substitute Sam Morrow in the 81st minute.
With a clear run on goal he easily brushed the ball past Tony Bullock to end the game with Terrors manager Ian McCall under even more pressure with his team at the foot of the table.