The Dons are now just three points off third place in the SPL
Aberdeen made it three home wins in a row to stake a late claim in the race for a Uefa Cup spot.
Richard Foster fired the Dons in front after Derek Young's shot had been beaten out by keeper Lukasz Zaluska.
Impressive defender Karim Touzani headed the home side further ahead from a corner early in the second half.
Danny Swanson replied with a fantastic run and shot to reduce the deficit but an entertaining match at Pittodrie did not yield any more goals.
The result leaves just three points separating the four teams chasing third spot in the SPL.
Aberdeen experimented with a back three of Touzani, Scott Severin and Andrew Considine and they were kept busy as United made the livelier start.
However, the visitors could not seriously threaten Dons keeper Jamie Langfield before falling behind against the run of play.
Young demonstrated a good burst of pace to leave Darren Dods trailing and his shot was parried by Zaluska into the path of Foster, who smashed in the loose ball from the edge of the penalty area.
Langfield then made a good save to keep out a powerful header from Lee Wilkie and Mark Kerr smacked a smart strike inches wide as United responded to the setback.
Touzani was on hand to clear a Noel Hunt effort off the goal-line after Langfield had lost the ball under pressure from the towering Wilkie.
And the keeper redeemed himself with a fine diving stop on the stroke of half-time to keep out Danny Grainger's dangerous free kick.
The Dons extended their lead early in the second half when Touzani met a deep corner from Jeffrey de Visscher and his downward header found the target.
But United hit back immediately thanks to a wonderful solo goal from Swanson.
The January signing from Berwick Rangers jinked his way past three opponents before firing home a great strike, via the post, from 20 yards.
Swanson then curled a fine strike inches wide of the goal, with Langfield well beaten.
The home fans were on their feet when Touzani struck a crisp shot through a congested penalty box but the ball whistled narrowly wide.
Zaluska got his fingertips to a Josh Walker free kick and the United keeper made another fine save to keep out a strong header from Lee Miller as Aberdeen finished strongly.
Young had a great chance to seal the win but dragged his shot wide, with the goal at his mercy.
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