City came flying out of the blocks as their bitter rivals came to town, going close several times in the opening minutes.
They weren't made to wait too long for their opener, either, as Silva struck gold with just 12 minutes gone.
As he so often is the classy playmaker was also involved in the build-up, feeding Raheem Sterling out on the left before continuing into the box.
Sterling's cross ran all the way through to the back post, where Bernardo Silva kept the ball alive and hook it back across goal, where his namesake took a touch before rifling beyond David de Gea to break the deadlock.
The goal was Sterling's third in his last three home games for City, the first time he has scored in three successive home games for the club.