The champions defended for most of the match, with Morata causing trouble for the City defence until he was subbed off early in the first half.
Manchester City went forward when Kevin de Bruyne shoot the ball into the top right corner after Silva's shot was blocked.
Chelsea mounted a late attack but could not get a goal.
Speaking after the game, Chelsea Manager, Antonio Conte said:
"It was a tough game but we know very well that Manchester City are a big team and it's very difficult to play this type of game.
"I think that we gave everything today and I am happy with the commitment and desire from all my players. They had the will to fight against a very strong team.
"In this type of game you need time to recover, if you are tired it is not simple to go box to box. Today we created chances but we didn't take them. Manchester City had chances and they took them.
"It is logical when you play three games in seven days you risk something. I hope it is not a serious injury for Morata. It is his hamstring but we don't know if it is a serious problem.
"We move on, we rest and I am very proud to be the coach of these players."
Manchester City Manager, Pep Guardiola, on his part, said:
"There are no words to describe what Chelsea are and what they did last season.
"It is important to win and especially with the way we played. In the first half we didn't find the right position but in the second we were better. A big congratulations for the victory.
"Chelsea want to play and they are so so dangerous in attack but we kept the ball and when they had it we pressed as high as possible.
"Everyone is talking about Kevin de Bruyne. He makes absolutely everythin. He is the most humble guy, I am so happy for him because I know how happy he is. Receive Instant News Update Via BBM: D3EDEFDF...Click HERE for Details. Share your story with us: firstname.lastname@example.org PLACE YOUR TEXT ADVERT BELOW:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> How I TOTALLY Got Rid Of my POT BELLY,excess Fat and Overweight In just 2weeks.. Click HERE for Details. Warning To Men: This 3 Foods Is Killing Your Erection. Click Here To Know Them