Ian McCall retained his unbeaten record in the SPL when his charges held out for a point despite being reduced to ten men for the last 20 minutes.
With three matches under his belt as manager, McCall has now witnessed a red card in each game.
It started so well for the hosts. After being so dominant, Jim Hamilton brought out the best from Julian Speroni in the 16th minute.
Stuart Duff's excellent run down the right was hit on the volley by the striker but the keeper somehow tipped the ball over the bar.
This only delayed the opener. Three minutes later, Charlie Miller arrowed a long ball for Hamilton and Jim McIntyre.
With Speroni coming out, there was a communication breakdown between him and David Mackay and the youngster headed it back into his own goal from 20 yards out.
Quite clearly, the visitors had been struggling with United's formation of playing Billy Dodds off the front two. The Dees, however, lifted themselves and responded well pressing for a penalty claim in the 25th minute for handball against Gary Bollan.
With this pressure, the Tangerines lead lasted only 11 minutes when the Dees equalised courtesy of yet another defensive mistake.
A long Fabian Caballero ball was completely missed by Bollan giving Nacho Novo the easiest of opportunities to slot home from 16 yards with Paul Gallacher committed.
This gave inspiration to the visitors as they matched United in the end-to-end excitement. Gallacher had to produce a superb point-blank save from Mackay's edge of box blast to prevent a certain goal while McIntryre edged in front of Speroni to head a whisker wide.
To reassert themselves, the Tangerines withdrew Hamilton and introduced Daniele Chiarini, moving Mark WIlson into midfield.
It was the hosts who had the first chance of the second half in the 53rd minute with Jamie Paterson's low 20-yard drive going narrowly past. One minute later, Novo created panic with a darting run that David McCracken mopped up at the death.
Astonishingly, it was three red cards in a row for United in the 69th minute when Charlie Miller foolishly picked up his second yellow card for handling after earlier being cautioned for persistent fouling.
With this piece of good fortune, Dundee really should have wrapped up the game. As it transpired, in what was a very disappointing second half, the Tangerines held on for a welcome point.