Dundee collected all three points against a battling United team who, despite being reduced to nine men early in the second half, made the Dark Blues work hard for their victory.
Good play by Barry Robson on the right saw him float a nice cross into the area which was met by Jason Scotland six yards from goal, but his header was poor and went well wide.
Just before the half-hour mark United won their ninth corner but again failed to put any great pressure on the home defence, and despite the visitors having almost all of the possession Kelvin Jack in the Dundee goal had not had a save to make.
Unfortunately for the Dundee keeper his home debut in the SPL ended moments later when he went off injured.
Mark Wilson saw his 25-yard effort easily saved by Dundee substitute Derek Soutar five minutes before the interval.
Seconds into the second half great play by Ian Anderson found Steve Lovell six yards from goal and only a superb block by Paul Jarvie denied Dundee.
The visitors were reduced to ten men in the 54th minute when Chris Innes was shown a red card for a last-man tackle on Lovell.
Five minutes later the visitors were astonishingly reduced to nine men when Mark Wilson was adjudged to have handled Garry Brady's long-ball forward.
United's nine men were doing well to restrict the home team to few chances and Robson should have done better than sky his shot over the bar on 70 minutes.
It looked like Robson had done much better moments later but his low shot went agonisingly the wrong side of the post.
Six minutes from time Callum McDonald headed just past the post as the home team grew desperate for a winner.
That winner came four minutes from time and it was one that young United keeper Jarvie will want to forget, as he allowed John Sutton's downward header to slip through his legs and roll over the line.