After a frantic opening nine minutes, typical of any derby, United created the first real chance through James Grady.
Running into space, the nippy little striker took a superb pass from Stuart Duff but saw Derek Soutar brilliantly parry his shot.
However, there was joy for Duff three minutes later when he scored the opener. Mark Wilson's cross was headed down by visiting defender Callum McDonald, and the midfielder pounced to slam the ball home from six yards.
Encouraged by this, the Tangerines continued to push forward for a second. Stevie Crawford's low cross flew across the goal-line and Jim McIntyre was only inches away.
But it wasn't all one way as Dundee valiantly tried to get back into the game. A thundering Lee Wilkie header after 26 minutes was booted off the line by captain Derek McInnes.
Four minutes from the break, debutant Nick Colgan denied Steve Lovell with a fine save before the injured Wilkie, replaced at the break, headed over from three yards on he stroke of half-time.
A last-gasp save from Soutar prevent United opening the second period with a second goal and the keeper, who had been in tremendous form all season, again foiled McIntyre 10 minutes later with a wonderful one-handed save, diving low into the corner.
But the Dees, who had been buildnig up pressure themselves, came even closer in the 58th minute when an acrobatic overhead kick from David McCracken on the goal line prevented Fabian Caballero equalising.
The Dees did finally draw level in the 71ist minute with a header from Tom McManus. Caballero darted down the right wing, curling in an inviting cross for the striker to edge in front of Colgan and nod the ball in from five yards.
As the game swung like a pendulum, United restored their lead eight minutes later, courtesy of McIntyre. The striker, who has a habit of scoring in a derby, latched on to the end of a Mark Wilson cross with a glancing header after the full-back had outstripped Caballero to the by-line.
Dundee equalised with a gift six minutes from time. A dreadful blunder between Paul Ritchie and David McCracken allowed the ball to slip by them into the path of Lovell, who stooped to nod the ball in from two yards