Raheem Sterling opened the scoring for the hosts after only nine minutes by blasting the ball past the keeper.
A stunning cross from Kevin De Bruyne then allowed Gabriel Jesus to double the Sky Blues’ advantage as he easily tapped the ball into the net to put his side in a comfortable position.
But the Italians who have won all eight of their domestic matches this season could not emerge victorious in this match although they were awarded two penalties, the first one of which Ederson saved before Amadou Diawara scored the second to make it 2-1.
With the triumph, Man City remain at the top of Group F of the Champions League taking a big step towards the knockout stages.