Luke Thomas opened scoring with a stunning volley past David De Gea, before Mason Greenwood levelled for United.
However, Caglar Soyuncu headed in the winner in the second half.
The result leaves United with 70 points from 35 matches, 10 behind City with three fixtures left.
Manchester City have three league fixtures remaining, before attention will turn to their first-ever Champions League final.
The club’s latest league title moves them on to seven in total, with Manchester United still out in front on 20.
- Daily Post