Stevie Crawford scored against his former club to help end Aberdeen's eight-week wait for a home win.
Crawford set up Jamie Smith for the opener, the forward finally rounding Derek Stillie after the goalkeeper had pulled off two fine, quick-fire saves.
Barry Nicholson's cross struck Richie Byrne's heel and fell into the path of Crawford, who bundled home the second.
Sub Gary Kenneth came closest for United after the break, but their unbeaten run ended after three games.
Andrew Considine had replaced the injured Kevin McNaughton in the Dons defence and Steve Lovell came in for Darren Mackie up front as boss Jimmy Calderwood switched from a 4-4-2 formation to three at the back.
Smith was given licence to roam behind Lovell and Crawford and it nearly paid immediate dividends.
Stillie could only parry Smith's powerful effort and Nicholson somehow sent his effort wide from eight yards out.
United, unchanged after Saturday's fine win away to Falkirk, slowly came into the game and David Fernandez blasted an effort across goal that Ryan Esson pushed away to safety.
Lovell had to be replaced with Mackie after picking up an injury and the replacement made an immediate impact by setting up Smith six yards out.
But the forward sent his side-footed drive wide only to go from villain to hero with his fifth goal of the campaign five minutes later.
Set up by Crawford, Smith had two efforts superbly saved by Stillie but finally wrong-footed the goalkeeper to roll the ball into the net.
The rampant Dons added a second before the break.
Nicholson's driven cross was deflected towards Crawford by Byrne and the Scotland striker bundled the ball into the net from 10 yards out.
United lost the experienced Paul Ritchie to injury early in the second half, with teenager Kenneth moving into defence.
Fellow substitute Collin Samuel made an immediate impact with a volley that tested Esson.
Samuel nearly netted an unlikely goal when his cross almost looped over the goalkeeper and into the goal, but Esson recovered to tip the ball over the bar.
The goalkeeper produced a magnificent diving save to thwart Kenneth, who connected with an in-swinging cross from Barry Robson.
A drive from Dons sub Gary Dempsey was deflected over the bar as the home side ended the game on top.
Aberdeen: Esson, Anderson, Diamond, Considine, Hart, Nicholson, Severin, Smith, Byrne, Crawford (Dempsey 78), Lovell (Mackie 24).
Subs Not Used: Langfield, Winter, Stewart, Muirhead, Foster.
Booked: Severin.
Goals: Smith 36, Crawford 43.
Dundee Utd: Stillie, McCracken, Archibald, Ritchie (Kenneth 58), Canero, Wilson, Brebner, Kerr (Samuel 63), Robson, McIntyre, Fernandez (Miller 75).
Subs Not Used: McInnes, Duff, Samson, Cameron.
Booked: Kerr.
Att: 10,720
Referee: C Murray