Second-half goals from Bernardo Silva and substitute Leroy Sane killed off a fired-up United side at Old Trafford and took City back above Liverpool at the top of the table.
City, who have won their last 11 league matches, now lead the Merseysiders by a point with three games remaining for both sides.
The match had long been identified as a tricky hurdle for City but with games against Burnley, Leicester and Brighton in their run-in, they will now be regarded as clear title favourites.
It was a victory Pep Guardiola’s side certainly had to work for and show all their champion qualities to achieve.
City’s win at Old Trafford saw several key talking points, including:
Speaking after the match, City captain Vincent Kompany said: “We didn’t start as well as we’d have liked it but that can happen.
“We defended well when we needed to and in the second half we got into our rhythm. In the second half we were there to score goals.
“It’s significant because it’s a derby. In the league, nothing is played out yet. Burnley is a difficult away game next and there is plenty to play for both for us and Liverpool. We will deal with the other games in the next days.
“We need three wins. We cannot expect the opponent to drop points. We’ll get back into our routine and if everyone does the right thing and this team prepares well we always have a big chance to produce a good performance.”
Meanwhile, goalscorer Leroy Sane heaped praise on Pep Guardiola’s words of advice at half-time that helped inspire them to victory.
“It was a difficult game. The first half we had problems but in the end we did it well. We were patient and played our game.
“Pep Guardiola always tries to help us to see what we did not so good, as well as what we did good, showing us examples [at half-time].
“In every game if you sit on the bench you hope to come on. Especially in the derby. I was waiting and hoping.
“When Raheem passed the ball I knew I had to react quickly.