On a thrilling afternoon in front a 14,000 full-house, John Souttar put the home side in front early in the second half, only for Barry Robson to equalise before Pawlett's late coup de grace.
Aberdeen had a great chance to edge ahead when Pawlett profited from Souttar's indecision but the Dons striker shot straight at Radoslaw Cierzniak.
Scott Vernon then got the better of Souttar, but was not quite able to pick out Niall McGinn in a dangerous position.
Dundee United threatened just before the break when Andrew Robertson saw his shot deflected wide of Jamie Langfield's goal.
Souttar (51) made the breakthrough as Langfield made a mess of Mark Wilson's corner and the United man reacted quickest to lash home his first goal for the club from six yards.
The travelling support were screaming for a second yellow card for Paul Paton after he clattered into Pawlett, but referee Willie Collum was unmoved.
But the match official was soon back in the Aberdeen fans' good books when he awarded a handball against Robertson and Robson levelled it up from the penalty spot (64).
McGinn then fired in a fine effort from the angle, but Cierzniak was equal to it with a fine stop and Pawlett also brought the best out of the United keeper.
The pressure kept building on Cierzniak's goal and the United resistance was broken when Robson's free-kick bounced off Nadir Ciftci into the path of Pawlett (90) who gleefully headed home the winner.