United jumped over Motherwell into fifth place in the SPL in what was a thrilling encounter in which either team could have scored a handful.
The hosts opened up in top gear with Derek McInnes and Jim McIntyre both testing Gordon Marshall before Charlie Miller forced the keeper into a great save with a low 16 yard shot in the sixth minute.
The home pressure continued with a Jim McIntyre header but it was not all one way.
Alex Burns brought panic in the 16th minute when he latched onto a Derek McInnes slip but he wasted the chance.
Chances continued aplenty but the bulk continued to fall to the Tangerines.
Barry Robson curled a 20-yard free-kick which the skilled Gordon Marshall pulled off an excellent save at the base of the post.
As half time came the visitors looked stronger, Steven Hammell's 30-yard drive forced Paul Gallacher to save brilliantly and touch it for a corner.
Then an Alex Burns low cross whipped across the goal without anyone taking it.
The away side continued to be on the attack after the break.
United boss Ian McCall admitted this by making a double substitution in the 62nd minute. Bringing on Billy Dodds and Jason Scotland. Amazingly it paid off when the Tangerines took the lead three minutes later. Billy Dodds' cross was headed by Jim McIntyre down into the path of Robson.
The midfielder's hooked shot was dropped by Gordon Marshall giving the Trinidad striker, the chance to ram the ball home in at the far post. The stunned visitors almost equalised soon after.
Shaun Fagen's 30-yard shot was heading into the top corner before Paul Gallacher touched it onto the bar and away to safety.
The game continued to be wide open with chances for both sides but mostly for The 'Well but, much to their frustration, Gallacher was in top form and the Tangerines managed to hold out for the victory.