A couple of half chances early on for Dundee saw Garry Brady and then Fabian Caballero both fire wide of the target.
The visitors came close on 17 minutes when a right-footed-free kick by Mark Wilson crashed against the crossbar.
The same player had another go from outside the area but this time his effort was weak and easily saved by Derek Soutar ten minutes from half time.
Five minutes before the interval another poor effort at goal by Tom McManus was easily saved by Tony Bullock.
Stevie Crawford volleyed just over the crossbar from close range early in the second period after he did well to control a Barry Robson cross.
With 52 minutes played, United took the lead and it was a disaster for the Dundee defence.
Wilson hit a low free-kick from the corner of the box which was missed by defender Callum McDonald and goalkeeper Derek Soutar before rolling into the far corner of the net.
With 20 minutes of the second half gone, Dundee levelled when they were awarded a penalty kick for a foul by Garry Kenneth. Steve Lovell stepped up and sent Bullock the wrong way from spot.
The visitors went back in front two minutes from time when Soutar did well to save Robson's shot but the ball broke to Jason Scotland who sent it back across goal to Jim McIntyre who bundled it home.
With three minutes remaining things went from bad to worse for the home team as McManus was shown the red card for a wild kick at Scotland as the United man stood with the ball at the corner flag.