Pep Guardiola's side ran riot at the Etihad Stadium despite a late consolation goal from Alvaro Negredo, taking the European champions to the top of group
Bayern's win was its club-record seventh Champions League victory in a row and it was Franck Ribery who put the reigning champions ahead seven minutes in before Thomas Muller made it two after the interval.
A first defeat at home for Manchester City boss Manuel Pellegrini was confirmed when the impressive Arjen Robben got in on the act just before the hour mark, with Alvaro Negredo grabbing the hosts' consolation late on prior to a red card for Jerome Boateng.
Micah Richards started for the first time under Pellegrini, while the Chilean was also able to name Sergio Aguero in his starting XI after the Argentina international missed Saturday's Premier League defeat to Aston Villa. David Silva was among the substitutes following his recovery from a thigh injury.
Meanwhile, Pep Guardiola opted to play Thomas Muller in an advanced role, replacing Mario Mandzukic, while Mario Gotze was named on the bench once more as he continues his return to full fitness following the ankle injury that he sustained during the Super Cup win over Chelsea.
David Alaba also made his 25th appearance in the Champions League, more than any other Austrian player in the competition's history.
Ribery caught City cold early on in the Group D clash as he edged the visitors ahead with a stunning long-range strike. The France international cut in from the left wing to beat Joe Hart at his near post and set the tone at the Etihad Stadium.
Toni Kroos then saw an effort deflected just wide 13 minutes later as Bayern continued to control proceedings.
Robben went close on the half-hour mark as he comfortably went past Matija Nastasic and fired across goal, though Muller was unable to get a touch and divert it home.
Bayern enjoyed 67 percent possession in the first half but it was the home side which began brighter after the interval, keeping the ball well without endangering Manuel Neuer's goal.
But Robben threatened again eight minutes into the half, with the Dutchman's effort from outside the area deflecting just wide of Hart's right-hand post.
And Muller doubled Bayern's lead five minutes short of the hour mark after evading Gael Clichy and calmly controlling a long ball from Dante.
With Hart looming, the Germany international rounded the City goalkeeper and tapped home to double the visitors' lead.
Sensationally, Bayern was three ahead within the hour as Robben capped a fine display with a deserved goal.
After a quick counter, Robben twisted Nastasic inside out before firing past Hart at his near post to put the Bundesliga champions out of sight.
Substitute Negredo pulled a goal back for the home side after being introduced for Edin Dzeko, however, the close-season signing turning neatly inside the area before curling an effort past Neuer.
Amd Boateng saw red for a foul on Yaya Toure four minutes from time, with substitute Silva striking the crossbar from the subsequent free kick. It mattered little, however.