The formidable attacking trio of Franck Ribery, Thomas Muller and Arjen Robben all struck as City were completely outplayed in Champions League Group D, although they also contributed to their own downfall.
Errors from goalkeeper Joe Hart and the defence proved costly but the hosts at least finished strongly as Alvaro Negredo replied and Bayern had former City defender Jerome Boateng sent off.
The result lifted Bayern clear at the top of the group and, even after just two games, probably left City in a battle for second place with their next opponents CSKA Moscow.
The overwhelming feeling was that a City side that thrashed Manchester United just 10 days previously were taught a footballing lesson.
Manuel Pellegrini was appointed by City in the summer in expectation he could improve the club's standing in Europe but this was clear indication of the scale of the task ahead.
Yet as brilliant as the Germans were, the defence and Hart had a harrowing time.
Hart was at fault for Bayern's opener and was beaten too easily for the third goal, while Gael Clichy was the chief culprit for the second.
City seemed intent on making a lively start but it soon became apparent that Bayern had the class to boss the game.
They carved out an early opening as David Alaba was given room to cross but Robben was unable to direct a header on target.
City showed some promise as Jesus Navas crossed for Micah Richards but the defender, surprisingly recalled in place of Pablo Zabaleta for the fixture, headed at Manuel Neuer.
Bayern firmly took control of the match in the seventh minute as Ribery cut in from the left and unleashed a low swerving shot from the edge of the area which Hart failed to deal with.
It was powerful strike but after a relatively serene spell for club and country for Hart - keeping five successive clean sheets in August and September - it was a mistake that will provide untimely ammunition to critics ahead of England's climactic World Cup qualifiers.
Bayern oozed class thereafter, barely giving City a kick as they dominated possession and cut their way through the hosts with quick and incisive passes.
Remarkably, it yielded few clear-cut chances in the first half but Hart punched unconvincingly from an Alaba cross and Toni Kroos had a long-range shot deflected narrowly wide.
Robben picked up possession on the edge of the area and drove across goal but Muller was unable to turn in.
Alaba then shot at Hart and the rebound off Matija Nastasic also needed to be dealt with by the keeper but City could consider themselves fortunate to reach the interval 1-0 down.
Bayern stepped up the pace after the break and Robben had a shot deflected wide from the edge of the area after more neat interplay.
City had also looked more determined after the resumption but their renewed spirit was killed off as Dante picked out Muller with a crossfield pass.
The City defence were simply caught flat-footed and Clichy stopped in expectation of an offside flag that never came, exposing Hart.
Muller seized the opportunity and rounded Hart to double the lead.
Just three minutes later the task was put completely beyond City.
Fernandinho lost the ball in midfield and Robben charged down the right, bypassing Clichy and wrong-footing Nastasic before beating Hart at his near post.
Muller hit the post as Bayern threatened more but City finally found some bite late on.
James Milner had a shot tipped over and fellow substitute Negredo pulled one back with a powerful shot off the post 11 minutes from time.
Boateng was shown a straight red card after halting a Yaya Toure burst on the edge of the area and David Silva curled the resulting free-kick against the bar.
Negredo also headed wide as City gave themselves some encouragement for the remainder of the campaign.
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