The holders were quickest off the starting blocks, almost breaking the deadlock in the 16th minute when Bastian Schweinsteiger's low shot came back off the post.
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Bayern came out swinging after the break, almost taking the lead in the 56th minute when Franck Ribery found himself clean through on goal, only to be denied by another good stop from Kozacik.
The German outfit's pressure paid off in the 65th minute when they took the lead through Mandzukic, who powered home a header from Philipp Lahm's cross.
Plzen's best chance to equalise came in the 76th minute as Petrzela's cross from over on the right flashed across the face of goal, narrowly missing Stanislav Tecl.
Gotze blew a golden opportunity to make the game safe in the latter stages, but one goal proved enough to seal maximum points for Bayern and fire them into the last 16 of the competition.