Two goals from Barry Nicholson and a predatory strike from Darren Mackie helped impressive Aberdeen heap more misery on under-fire Dundee United boss Craig Brewster.
Mackie opened the scoring seven minutes before the interval and Nicholson doubled that advantage shortly after the restart with a well-placed free-kick.
Barry Robson pulled a goal back from the penalty spot after a foul by Russell Anderson on Craig Conway, but within a minute the Dons secured all three points courtesy of Nicholson's second.
Despite deploying an adventurous formation, it took until the 13th minute for Aberdeen to offer an attacking threat as Richard Foster first shot wide from distance before Jamie Smith saw an effort deflect off David McCracken and roll just wide of the post.
From Nicholson's resultant corner, Anderson won a header in the United penalty area and Chris Clark's subsequent shot was comfortably dealt with by Derek Stillie in the visitors' goal.
The home side were now looking more dangerous and shortly afterwards Mackie sent a clipped centre across the face of goal, but frustratingly for Aberdeen there was nobody in the middle to turn the ball into the empty net.
For the most part, United were forcing Aberdeen into shots from distance and Clark's effort from 30 yards drifted just wide.
With the away side concentrating on defence they offered little up front, until David Proctor forced Jamie Langfield into making a great save in the 37th minute courtesy of a stooping downward header following Robson's cross.
Aberdeen responded to that scare immediately though and a minute later broke the deadlock.
Nicholson's drive from 25 yards drew a block at full stretch from Stillie, but the ball rolled straight into the path of Mackie who gleefully rolled the ball into the net to score the 100th league goal since Jimmy Calderwood took charge at Pittodrie in 2004.
Buoyed by that strike, the home team nearly doubled their advantage with five minutes remaining before the break.
However, Mackie just failed to get a touch on Clark's searing shot and Aberdeen had to be content with a one-goal lead at the interval.
The Dons made the perfect start to the second half though, when Nicholson's arcing free-kick from the left-hand corner of the United penalty area drifted over the head of a stranded Stillie and curled into the top corner of the net.
Scott Severin then came close with another free-kick from distance before Stillie did well to block a thumping drive from Dempsey in the 67th minute.
However, for all Aberdeen's attacking threat United were handed a lifeline three minutes later when an innocuous challenge from Anderson on substitute Conway resulted in a penalty for the visitors.
The decision by referee Craig Thomson was certainly controversial, but nonetheless Robson stepped up to drill the ball low past Langfield from the spot.
Clearly angered at conceding that goal, Aberdeen roared forward from the kick-off and immediately restored their two-goal advantage.
Richard Foster's cross from the left was headed in by Nicholson at the far post.
Substitute Chris Maguire nearly put the icing on the cake for the Dons late on, but his effort was ruled out for offside as a poor United side suffered their third defeat in a row.
Teams:
Aberdeen: Langfield, Anderson, Severin, Hart, Nicholson,Dempsey, Jamie Smith (Maguire 77), Clark, Foster, Miller,Mackie (Considine 85).
Subs Not Used: Soutar, Winter, Macauley, Donald, Paton.
Booked: Jamie Smith, Anderson, Hart, Clark.
Goals: Mackie 39, Nicholson 47, 71.
Dundee Utd: Stillie, McCracken, Archibald, Mair,Kalvenes (Duff 46), Proctor, Kerr (Conway 57), Cameron, Robson,Hunt (Goodwillie 57), Samuel.
Subs Not Used: McLean, Kenneth, Gardiner, Easton.
Booked: Duff.
Goals: Robson 70 pen.
Att: 10,747
Ref: C Thomson (Scotland).
