After dominating much of the first half the Dons conceded a bizarre penalty kick on 47 minutes when new signing Tommy Wright stupidly handled inside the area.
Dundee United boss Craig Levein was a relieved man following the match which saw his side record their first SPL win since March 2008.
Aberdeen opened brightly with Sone Aluko prominent on the left. However, his final ball failed to trouble the visitors' centre-backs Lee Wilkie and Darren Dods.
The home side ought to have gone ahead on eight minutes when Lee Miller's poor free-kick deflected into the path of Gary McDonald who from only seven yards out screwed his left-foot effort wildly over.
At the other end United threatened on ten minutes. Craig Conway scampered down the left before playing a great ball to the far post where Jon Daly stretched but could only guide his effort wide of the upright.
Aberdeen came close again on 22 minutes. Charlie Mulgrew's accurate corner found the head of Lee Miller, but his effort flew narrowly over the crossbar.
A smart counter-attack by United four minutes later led to Richard Foster heading desperately over his own crossbar with Daly lurking inside the area.
On 35 minutes Prince Buaben fed Scott Robertson who let fly from 22 yards but his shot narrowly missed the target.
As the game entered the final minutes of the half Chris Maguire's stinging shot was parried by Lukasz Zaluska. Wright looked to have the easy task of knocking the ball home, only for Sean Dillon to appear from nowhere and charge down the big striker's efforts.
The ball broke to McDonald who carelessly drilled the ball over.
United were literally handed a gift immediately upon the restart when Wright needlessly put hand to ball inside the area, giving referee Callum Murray the easy decision to award a penalty kick. Striker Francisco Sandaza calmly slotted the resultant spot-kick home.
The game could have been over as a contest on 52 minutes. Sandaza picked out strike partner Daly who had peeled away from his marker. However, the forward failed to get the awkward cross ball on target.
Great play by Foster and Mark Kerr created an opening for Wright but his tame shot went the wrong side of the post.
Aberdeen were pushing hard for an equaliser and they came very close again on 76 minutes. Alexander Diamond headed Mulgrew's corner back across the area where second-half substitute Darren Mackie was denied by Zaluska's point-blank save.