Franck Ribéry, Thomas Müller and Arjen Robben all struck with City goalkeeper Joe Hart culpable for all three goals as his poor form worsens.
Alvaro Negredo hit an excellent consolation but just like two years ago the Bavarians were too good for City. CSKA Moscow beat Viktoria Plzeň 3-2 in the other group game.
Manchester United were denied victory by Taison's 76th minute strike during a reticent draw with Shakhtar Donetsk. Danny Welbeck opened the scoring after 18 minutes. Elsewhere in Group A, Bayer Leverkusen earned their first win in the competition thanks to Jens Hegeler's stoppage-time winner.
Roberto Mancini's first match in charge of Galatasaray was a lively affair as the Turkish champions drew 2-2 at Juventus.
Didier Drogba gave Gala the lead but an Arturo Vidal penalty and Fabio Quagliarella goal put Juve 2-1 up before Umut Bulut levelled two minutes before time.
Real Madrid made it two wins out of two with a 4-0 thrashing of Copenhagen. Cristiano Ronaldo and Angel di María scored two apiece there.
And finally, Paris Saint-Germain and Olympiakos dished out 3-0 beatings to Benfica and Anderlecht.