Michael Carrick was given the task of leading United for the rest of the season this week after Portuguese Ruben Amorim was fired.
The former United midfielder has previously served as an interim coach and assistant at the club.
He made five changes compared to the United team that lost to Brighton in the FA Cup last weekend.
And it was a full-strength United that took part in the derby at Old Trafford.
Already in the third minute, Harry Maguire had a header hit the crossbar.
Manchester City, second in the Premier League, had an injury crisis in the back line - three center-backs were missing - and it was noticeable in the derby. City had the ball, but United created dangerous chances throughout the game.
Even before halftime, the team had the ball in the City goal twice - but both Amad Diallo and Bruno Fernandes were ruled out for offside.
City goalkeeper Gianluigi Donnarumma kept City in the game for a long time.
But eleven minutes into the second half, the home team were rewarded through Bryan Mbeumo and Patrick Dorgu.
Amad Diallo was just inches away from a 3-0 goal, but hit the post in the final minutes.
United's victory was their first in the Premier League since Boxing Day.
