The 10-man Dons also kept the pressure on Scottish Premiership leaders Celtic with the win as they moved to within five points of the Hoops.
Adam Rooney’s 27th goal of the season six minutes before half-time was enough to seal the win and a deserved three points for the home side.
The visitors never looked like building on last week’s home win over Hamilton, which ended a five-game losing streak, even when Barry Robson was sent off for an alleged elbow on Charlie Telfer after 70 minutes.
The hosts forced the first effort less than five minutes in when Rooney latched on to Mark Reynolds’ ball over the top before laying it off for Kenny McLean who could only blast the ball over the bar.
They threatened again 10 minutes later when McLean picked out Jonny Hayes but the striker’s effort was well saved by Radoslaw Cierzniak in the United goal.
Aberdeen were well on top but were struggling to capitalise on possession and chances. Niall McGinn was next to try his luck when he took advantage of a poor clearance by United but slipped and his effort did not trouble Cierzniak.
The home side eventually broke the deadlock just before before half-time. Robson’s free-kick was met by Reynolds, who was denied by Cierzniak, but Rooney was on hand to follow up from the rebound.
Although Aberdeen goalkeeper Scott Brown was called into action on the brink of half-time to deny United, the home side deserved their lead at the break.
Polish ‘keeper Cierzniak then had to be alert after the interval to deny Willo Flood as Aberdeen pushed for a second.
Chris Erskine, who had scored the winner the week previously against Hamilton, nearly pulled United level soon after when he cut through the Aberdeen box before forcing Brown into a save.
The home supporters were forced to endure a nervy final 20 minutes when referee Bobby Madden showed Robson his 13th career red card after adjudging him to have elbowed Telfer.
However, the Dons held on to ensure that they will play European football again next season.