The first Tayside derby of the season ended all-square after the visiting side had completely dominated the opening period, but the Terrors responded in the same vein in the second half.
A determined start from the visitors saw Paul Gallacher's goal under tremendous pressure in the opening minutes. Following a near miss by Nacho Novo, only an excellent reflex save from the keeper prevented a Fabian Caballero goal.
The game then burst into controversy in the 20th minute when referee Mike McCurry awarded a soft penalty against David McCracken for pushing Novo.
The Spaniard appeared to fall easily much to the anger of the United defence, but the striker ignored the protestations and converted the kick himself, sending Gallacher the wrong way.
This rattled the Tangerines and, with their midfield beginning to dominate proceedings, Dundee really should have added to their tally by the half-hour mark.
United however, kept their opponents pegged back and almost equalised on the stroke of half time. Andy McLaren teased Jonay Hernandez before crossing for Craig Easton, but the striker wastefully ballooned the ball from eight yards.
United began the second half with more penetration. The warning signals were there for Dundee and after a few near misses the Tangerines deservedly equalised in the 56th minute.
Jamie Paterson flew down the wing and crossed for Jim McIntyre to head just inside the post past the sprawling arms of Julian Speroni.
Dundee responded to this concession in a positive fashion and were nearly gifted a goal two minutes later when Gallacher spilled the ball after both he and Chris Innes went for a cross.
The game had well and truly come alive and McLaren, United's best player, just chipped over as he struggled for the ball with Lee Wilkie.
As the game picked up pace, Caballero almost benefited from a freak goal when his cross flew off the boot of Mark Wilson and smacked the face of the bar.
Then the same player went down for a penalty in the 76th minute, but his claim was waved away in favour of a corner.
Twice Gallacher's brilliance thwarted Dundee in the 79th minute. Firstly from a Mark Fotheringham blast and then Fabrizio Ravanelli's header.
Meanwhile, at the other end, Owen Coyle went very close twice, both with headers and Innes fired in another header, but in the end neither team could find the net.