Michael Carrick was given the task this week of leading United for the rest of the season 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 to the United team that lost to Brighton in the FA Cup last weekend.
It was a fully fledged United side at Old Trafford in the derby.
Already in the third minute, Harry Maguire's header hit the crossbar.
Big brother City, second in the Premier League, had an injury crisis at the back - three centre-backs were missing - and it was noticeable in the derby. City had the ball, but United created good chances throughout the match.
Even before the break, United had the ball in City's goal twice - but both Amad Diallo and Bruno Fernandes were ruled out for offside. Another goal by Mason Mount in added time was ruled out after a VAR check.
City goalkeeper Gianluigi Donnarumma kept City in the game for a long time.
But in an eleven-minute spell in the second half, the home team's reward came through Bryan Mbeumo in the 65th minute and Patrick Dorgu in the 76th minute.
United's victory was their first in the Premier League since Boxing Day, and after dropping points against bottom teams like Wolverhampton, Burnley and Leeds, it was a significant scalp.
"Stability is the key to success. If you can find that, you'll be a winner, that's our challenge, to find a way to get there," says Carrick.
