Erling Haaland made the breakthrough midway through the first half with a powerful header from Antoine Semenyo’s cross.
The Norwegian went close to adding to his tally of three goals in three games while Rayan Cherki went close with a strike that smashed the inside of the post.
Newly-promoted Coventry had their chances too and Gianluigi Donnarumma made fine saves to deny Loum Tchaouna and Ellis Simms in the second half.
Elliot Anderson was named man of the match after a breathless display while fellow new signing Enzo Fernández and Iliman Ndiaye made their debuts.
Ayyoub Bouaddi and Ryan McAidoo also got their first taste of Premier League action at the Etihad as we made it three wins out of three.
Watch the best of the action in the video above…