Gabriel Jesus scored the only goal of the game to seal a richly-deserved win.
It was Pep Guardiola’s 221st victory as City boss – more than any other manager in the Club’s history.
The result means City are second in the embryonic Premier League table, with 13 points from our first six matches.
Liverpool, who sit top, are also on 13, but they have played one game fewer.
And you can watch highlights of the game above!
Our difficult week continues with a trip to Paris Saint-Germain in Group A of this season’s Champions League on Tuesday. City are looking to build on our 6-3 win over RB Leipzig on Matchday 1. PSG started with a draw against Club Brugge. Kick off in Paris is 20:00 UK time.
And then next Sunday, we travel to Anfield to face a rejuvenated Liverpool side in the Premier League. That game gets under way at 16:30 UK.
You can follow both of those games in detail on ManCity.com and the official Man City app.
Live text updates get under way two hours before kick off, before Matchday Live gets going around 45 minutes later.