United won, which means they will play in the Europa League. They finished eighth in the Premier League this season, 31 points behind champions City.
The Red Devils went ahead when Alejandro Garnacho scored from close range in the 30th minute. This happened after City defender Josko Gvardiol and goalkeeper Stefan Ortega got mixed up.
After nine minutes, Kobbie Mainoo scored a clinical goal to make it 2-0 to United.
Just before that, United had a goal taken away because Garnacho was offside when Marcus Rashford slid the ball home.
City got a goal back late in the second half thanks to Jeremy Doku, but United held on to win and get revenge for losing the FA Cup final last year.
With the win, the team, which came in eighth in the Premier League this year, has secured a spot in the Europa League. They were 31 points behind champions City.
There are also rumors that United manager Erik ten Hag is going to be fired soon because the team had a bad season in the English Premier League.
Even if United had won, they would not have been in Europe next season.
Some United players got down on their knees to celebrate on the field after the win, while others ran over from the technical area.