The German side dominated from the kickoff as a shot from distance from Franck Ribery was parried by Plzen keeper Matus Kozacik but only into the path of Mario Mandzukic, who somehow managed to miss the target from yards out with a headed effort.
However, Pep Guardiola's side did take the lead in the 25th minute from the penalty spot as Robben was brought down in the area by a clumsy tackle from Roman Hubnik. Ribery made no mistake from the spot, slotting his shot into the bottom corner.
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Kozacik kept Bayern from doubling their lead when Daniel van Buyten powered a header at goal but the keeper managed to keep it out with a one-handed save but that only delayed the inevitable as Alaba got his side's second, cutting in on his right foot and he curled a shot into the bottom corner.
It should have been three just before the break but Robben couldn't find the net as Kozacik denied his powerful left-footed shot with a good dive and he managed to beat the ball away with his left hand.
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After the break, Bayern soon got the crucial third goal with a fine move and finish from Ribery, who notched his second goal of the game as he drifted pass two defenders before lifting the ball over Kozacik into the net.
Guardiola's side were in cruise control after that and went further ahead when substitute Mario Gotze teed up Bastian Schweinsteiger on the edge of the area, and he turned and fired a shot into the top corner of the net.
Bayern were comfortable sitting on their lead for the majority of the game until the 84th minute when Gotze weaved his way down the right again and this time found Robben but the winger failed to make solid contact with the ball and scuffed his effort.
The home side rounded the game off with a fifth goal as Gotze raided forward down the right and got in behind the last defender to fire a shot into the top corner to seal a comfortable win for Guardiola's men.