The result left United second on 70 points from 34 games, 10 behind City who have played a game more and missed a chance to secure the title after they suffered a 2-1 home defeat by Chelsea.
It also stretched United's unbeaten away league run to 25 games but came at a cost as manager Ole Gunnar Solskjaer revealed captain Harry Maguire may be ruled out of the Europa League final against Spanish side Villarreal on May 26.
West Ham United blew their chance to apply real pressure in the race for a Premier League top-four finish as they slumped to a 1-0 home defeat by an Everton side who maintained their European qualification hopes.
Dominic Calvert-Lewin's 24th-minute goal proved decisive against a West Ham side who huffed and puffed but never really hit their stride on a crucial afternoon.
Morgan Gibbs-White's late strike earned Wolverhampton Wanderers a 2-1 comeback victory against 10-man Brighton & Hove Albion in a drama-filled Premier League encounter at Molineux.
Lewis Dunk fired the visitors ahead in the 13th minute, but the Brighton captain was dismissed early in the second half for a last-man challenge on Fabio Silva, turning the game on its head.
The hosts took full advantage of the extra man and drew level in the 76th when substitute Adama Traore fired home from close range after a neat one-two with Silva.
Gibbs-White, who had spurned a gilt-edged opportunity just minutes earlier, sealed the victory in the 90th when he smashed an effort from the edge of the penalty area perfectly into the top corner for his first Premier League goal.