Franck Ribery struck twice, to go with efforts from David Alba, Bastian Schweinsteiger and Mario Goetze at the Allianz Arena.
The result makes it three wins from three for the Bavarians, who set the pace in Group D with nine points, three ahead of second-placed Manchester City.
The Citizens beat CSKA Moscow 2-1 earlier in the night thanks to a brace from Sergio Aguero, with Zoran Tosic scoring the opener for the hosts at Luzhniki Stadium.
City's neighbours Manchester United edged Sociedad 1-0 at Old Trafford, courtesy of an early own goal from Inigo Martinez.
The Red Devils top Group A with seven points from three games, one point ahead of Bayern Leverkusen and three in front of Shakhtar Donetsk.
Leverkusen thumped Shaktar 4-0 in their fixture, with Stefan Kiessling netting either side of strikes from Simon Rolfes and Sidney Sam at BayArena.
Meanwhile, Real Madrid needed a Cristiano Ronaldo double to see off ten-man Juventus 2-1 in Group B, with Giorgio Chiellini getting sent off after the interval. Fernando Llorente equalised at one stage for the Old Lady.
The result leaves Los Blancos top of Group B with maximum points from three games, with Galatasaray and Juve five and seven points short of the summit respectively.
Galatasaray defeated bottom-placed FC Copenhagen 3-1 via goals from Felipe Melo, Wesley Sneijder and Didier Drogba. Claudimir scored a late consolation for the Danish visitors.
Anderlecht 0-5 Paris St Germain
Benfica 1-1 Olympiakos