Darren Mackie had given Aberdeen the lead at Pittodrie on Saturday with his first SPL goal of the season after eight minutes when he expertly chipped the ball over Dusan Pernis before United captain Jon Daly levelled when he volleyed home from a Willo Flood corner just before the half hour mark for his 21st strike of the season.
But Chris Clark pounced upon an error by Pernis to restore Aberdeen's advantage after 68 minutes before Ryan Jack's header 10 minutes later meant United's six-game winning run in the league would end with a whimper.
The Dons welcomed back Jack after illness and Stephen Hughes following his recovery from a hamstring injury.
Captain Russell Anderson and Iceland international Kari Arnason had to be content with a place on the bench, while winger Peter Pawlett missed out through injury.
United were unchanged from the team that defeated Dunfermline 3-0 last weekend with Keith Watson returning from injury to take his place on the bench.
The match began after a one minute's applause in memory of former Dons captain Jens Petersen who died recently in Denmark.
United had a strong appeal for a penalty turned down after only eight minutes when Clark Robertson looked to have tripped midfielder Scott Robertson in the box but referee Calum Murray waved play on.
And the home side took full advantage of that decision going in their favour by opening the scoring four minutes later when Mackie showed a great touch to dink the ball over Pernis in the United goal.
John Rankin curled the ball over the crossbar from the edge of the area after 22 minutes as the visitors tried to get back on level terms.
United almost gifted Aberdeen a second when Flood's careless back pass went straight to Hughes but the former Motherwell midfielder's powerful shot was well stopped by Pernis.
United equalised after 29 minutes when Flood's corner fell to the unmarked Daly who smashed the ball on the volley low past Aberdeen goalkeeper Jason Brown.
The Dons had a chance to regain their advantage just before the break when Clark's deep cross picked out Mackie but the striker was unable to direct his header on target.
United had an early chance in the second half when Daly was fouled by Andrew Considine on the edge of the area but Paul Dixon could not find the target with the resulting set-piece.
The frantic pace continued as Mackie went close to adding a second at the other end but his downward header from a Robertson cross was comfortably gathered by Pernis.
The Dons were forced to make a change after 55 minutes when Considine limped off and was replaced by Anderson for his first appearance at Pittodrie since rejoining the club.
Aberdeen regained the lead after 68 minutes courtesy of a poor error by United goalkeeper Pernis who fumbled a Rory McArdle cross and Clark slotted the ball into the unguarded net.
United brought on Danny Swanson and Stuart Armstrong for Flood and Gary Mackay-Steven as they looked for a creative spark to get back in the game, while Arnason replaced Hughes for the hosts.
But it was the Iceland midfielder who made the immediate impact when his long throw into the box was headed home by Jack after 78 minutes.
The result gave the Dons a clean sweep over United, having already beaten them in both of their previous league encounters this season.