Stewart scored Dundee’s opener before he set up James McPake and Paul Heffernen as the hosts recorded victory in a fiercely competitive derby at Dens Park.
A frantic opening saw Dundee earn a flurry of early corners before Jim McAllister’s long-range shot forced United keeper Harold Cierzniak into the game’s first save after seven minutes.
But they didn’t have to wait long to open the scoring following a glaring error from the normally dependable Cierzniak. Greg Stewart, who had drawn a save from the keeper moments earlier, gave Dundee a 14th-minute lead when his fanciful effort was allowed to trickle in by Cierzniak.
But United hit back straightaway when referee John Beaton penalised Dundee’s Kevin Thomson for a handball in the 16th minute when the midfielder threw himself in front of Sean Erskine’s shot.
Nadir Ciftci calmly dispatched the penalty and was promptly booked by referee Beaton after blowing kisses at the Dundee fans in celebration.
Stewart tested Cierzniak with another shot on target before Erskine forced a save from Scott Bain at the other end as the midway point of the first half approached.
But Dundee regained the lead in their 23rd minute when McPake rose to meet Stewart’s cross and headed past Cierzniak despite the Pole getting a hand to it.
Bain had to be at his best to deny United another equaliser after saving Jaroslaw Fojut’s point-blank header moments later before Aidan Connolly had a shot from a tight angle that drifted over.
United began the second half with intent, with Erskine having a shot blocked before Ciftci drew another fine save from Bain just after the hour mark.
But they fell further behind in the 68th minute after a sharp counter-attack from the home side. Stewart burst down the left flank before a measured low cross split the United defence, allowing Heffernen to slot home at the far post.
Dundee almost extended their lead nine minutes later but Stephen McGinn’s header was saved by Cierzniak.
United forced a flurry of corners as they chased the game but their efforts were in vain as Dundee avenged the 6-2 New Year’s Day defeat to claim their first derby win in eight games.