The Bundesliga champion could have been out of sight by half time but had only a Franck Ribery penalty and a
But two goals in three minutes from Ribery and Bastian Schweinsteiger and a late strike from Mario Gotze moved Pep Guardiola's men three points clear of Manchester City at the top of Group D.
Bayern was lively right from the start and
The competition holder continued to press and just a minute later, when
Bayern was relentless and Mandzukic had another chance to score as
Robben was next to threaten as he toe-poked Marcio Rafinha's cross wide at the back post and the host side could easily have been four up inside the opening 10 minutes.
Kozacik was having a busy night and was called into action as Alaba and Ribery combined and he was forced to turn the Frenchman's effort round the post.
But there was little he could do to prevent the opener in the 25th minute as
The defender was booked for his trouble and Ribery stepped up to dispatch the spot kick into the bottom corner.
Two minutes later Mandzukic should have doubled the lead as good build-up play from Robben found him alone in the penalty area but he could only fire straight at the goalkeeper.
Kozacik was keeping his side in it and was forced into a brilliant save just before the half hour when
The Slovakian denied Schweinsteiger just moments later but Bayern's dominance brought them a second goal eight minutes before the break.
Schweinsteiger found Mandzukic who headed the ball into the path of Alaba and the 21-year-old controlled with his chest, beat his man and then rifled home with his right foot.
It was not long before Bayern found its stride again after the break and two goals in three minutes well and truly ended the game as a contest.
First, in the 61st minute, Robben and Mandzukic exchanged passes before finding Ribery who cut inside and audaciously scooped the ball over Kozacik's head and into the back of the net.
Gotze was then brought into the action and, just a minute after coming on, he set up Schweinsteiger for the fourth as the
Plzen had its first corner in the 67th minute but Bayern soon countered and Gotze hit the crossbar with a chip from a tight angle.
He was determined to score and got his goal in injury time as he showed sublime close control at the back post and slotted home.