In condemning City to their heaviest-ever home defeat in Europe, Pep Guardiola's slick Bayern side extended their winning streak to seven matches on the continent with a polished performance at the Etihad Stadium that was more comfortable than the 3-1 scoreline suggests.
England goalkeeper Joe Hart should have kept out Franck Ribery's raking effort from distance on seven minutes before Thomas Mueller benefited from some horrid City defending to round Hart in adding the second on 56 minutes.
Robben bounded beyond Matija Nastasic to slam a shot into the corner of the net via a post with Hart failing to keep the shot out when he should have done better. He is the first Bayern player to score in five successive games in the tournament.
Mueller saw a shot come back off the post as City continued to be outclassed operating with an ill-advised 4-4-2 formation under new coach Manuel Pellegrini.
Home substitute Alvaro Negredo scored a fine consolation goal on 79 minutes before former City man Jerome Boateng was sent off for a late challenge on Yaya Toure as he seemed likely to race in on goal.
David Silva saw the free-kick come back off the post, but a second home goal would have put a false gloss on a night when the English side were well beaten by Bayern's high-tempo pressing game. Bayern top the section with six points from two games.
7' - RIBERY OPENER: Ribery smashes a shot into the net from distance. Hart couldn't keep it out despite seeing it all the way. Poor goalkeeping really by Hart. Bayern lead 1-0.
29' - ALABA UNLUCKY: Alaba sees a venomous volley come back off the chest of Matija Nastasic and land in the arms of Hart. That could have ended up in the back of the net.
56' - MULLER MAKES IT TWO: Mueller takes the ball beyond Hart from Dante's long ball to net. Clichy well out of position. A 2-0 lead for Bayern. Awful defending by the home side.
59' - RAMPANT ROBBEN: Superb stuff from Bayern as Robben goes beyond Nastastic. Drills the shot into the corner of the net. And that is a 3-0 lead. Once again Hart at fault.
74' - MULLER MAGIC: Mueller so unfortunate to see crisp shot come back off a post with Hart well beaten. Almost a 4-0 lead.
79' - NEGREDO CONSOLATION: Fine turn and finish from Negredo with Boateng not picking up. In off the post. City back to 3-1 behind.
85' - BOATENG RED: Boateng late on Yaya Toure and he is off the park. Last man tackle. Had to go.
86' - SILVA FREE-KICK: The Spanish midfielder sees a free-kick come back off the bar. So unfortunate. Just couldn't get the ball back down in time.
TALKING POINT: Can Bayern become the first club to win back-to-back Champions League trophies? Very much so. They will take some stopping on this display, but injuries and suspensions later in the season will be crucial. The German champions are a team in every sense of the word.
Thomas Mueller has now scored four goals in his last five Champions League appearances.
Arjen Robben is the first Bayern player in Champions League history to score in five successive games.
This is the first time Man City have ever conceded 3+ goals in a European home game.
Bayern's opener means that all six away teams to have played a Champions League game at the Eithad have scored.
Every single Bayern outfielder made more passes than City's busiest passers in the first half (Nastasic/Fernandinho, 16).
Franck Ribéry's goal was his first in 12 Champions League appearances.
MANCHESTER CITY: Hart 4, Richards 5, Kompany 6, Nastasic 4, Clichy 4, Toure 5, Fernandinho 5, Navas 4, Nasri 4, Aguero 5, Dzeko 5; Subs: Milner 6, Silva 7, Negredo 7
BAYERN MUNICH: Neuer 7, Boateng 5, Rafinha 7, Dante 7, Alaba 7, Lahm 8, Schweinsteiger 9, Kroos 8, Robben 9, Mueller 8, Ribery 9; Subs: Shaqiri 6, Kirchhoff 6, Götze 6
MAN OF THE MATCH
Arjen Robben (Bayern Munich) - Wonderful stuff from the Dutchman, but Ribery, Philipp Lahm and Bastian Schweinsteiger could all have got the nod.
THE MATCH IN A TWEET