Robbie Muirhead’s first goal for United after 13 minutes was enough to kill off any hopes the Dons had of catching the Hoops at the top of the table.
Celtic had beaten Dundee 5-0 on Friday evening to ensure that Aberdeen had to take maximum points on Tayside to keep the title race going.
However, despite dominating possession for spells of the game, the Dons just couldn’t convert their chances after Muirhead’s opener.
Aberdeen had the first chance after just two minutes but Adam Rooney couldn’t direct his header on target.
Rooney went close with his head again just a few minutes later but Radoslaw Cierzniak made a good save to deny the striker.
The away side may have started brighter but it was United who took the lead when John Souttar picked out Muirhead to smash home his first goal for the club.
Ashton Taylor tried to respond immediately for Aberdeen but he flashed his header just wide.
The visitors were then dealt a blow when Peter Pawlett had to be replaced after just 24 minutes when he failed to recover from a nasty head knock, being replaced by Cameron Smith.
Aberdeen enjoyed more of the possession but struggled to carve out clear cut chances and they nearly paid for that when Nadir Ciftci forced a save from Scott Brown in the Aberdeen goal just after the half hour mark before Muirhead went close again, firing just over.
Goalscorer Muirhead continued to look dangerous after the break, forcing Brown into a good save with an effort from just inside the box.
United substitute Aidan Connolly could have made it 2-0 to the home side but he fired over.
Aberdeen knew they had to win to keep their slim title hopes alive and went searching for an equaliser but neither Smith nor Niall McGinn could get on the end of Jonny Hayes’ driven cross.
United keeper Cierzniak then had to look lively to twice deny Rooney and preserve his side’s lead before the Dons striker went close with an acrobatic overhead kick.
Taylor had a late chance to force an equaliser for the Dons but he could only head into the side netting at the back post.