It would prove to be a difficult night for the hosts as they struggled to break down Manuel Pellegrini's side, but a Jerome Boateng effort which hit Mario Gotze on the way into the back of the net was enough to hand Bayern three points.
Below, Sports Mole takes a look at the key talking points from the match.
On target: 8
On target: 2
Was the result fair?
It's certainly a difficult one to judge, but on the balance of play, Bayern probably did enough to collect all three points. On another night, City would have picked up a point, but most of their work did come in defensive areas and they were fortunate not concede much earlier in the game.
Pep Guardiola's side were well short of their fluent best, and they'll surely improve as they progress in the Champions League. As expected, they dominated possession and always looked comfortable on the ball. However, they lacked a cutting edge we're used to seeing from them. When the ball was worked to the likes of Juan Bernat and Rafinha in wider positions they looked more dangerous, but it was clear they missed Franck Ribery and a fully fit Arjen Robben.
Man City's performance
It almost sounds like a patronising thing to say about the Premier League champions, but the visitors really did perform admirably under pressure inside the Allianz Arena. They would expect to cause more problems going forward, but Sergio Aguero was left on the bench, and Yaya Toure just could not get into the game. It will come as little consolation to say just how good Vincent Kompany and Martin Demichelis were in the centre of defence, but that pair and Fernandinho really did stand out, despite the disappointing loss.
Sports Mole's man of the match
David Alaba: In truth, it wasn't really a night for individuals. However, Alaba produced an excellent display all over the pitch as he moved seamlessly from defence to midfield in the first half to contribute to his side's win.
A tough choice tonight, but Arjen Robben frustrated the neutrals again with a blatant dive under pressure from Fernandinho late on. His critics will love to see a replay of the incident.
Alberto Undiano Mallenco was strong enough to wave away protests when Bayern appealed for a penalty on a couple of occasions, but he probably should have pointed to the spot when Mehdi Benatia brought down David Silva in the second half.
Bayern: Guardiola's men are back in Bundesliga action against Hamburger SV on Saturday afternoon.
Man City: Another tough task awaits Man City when they host Chelsea on Sunday.