On the day Bayern's players make their annual appearance at the city's beer festival, a sobering performance was enough to earn Bayern all three points and keep them on the same number of points as league leaders Borussia Dortmund, albeit without improving their goal difference.
Muller's goal after just over an hour was the only difference between the two sides, although Bayern will have to do better at Manchester City in midweek if they are to remain unbeaten this season.
Former Bayern midfielder Luiz Gustavo went close to shocking the home fans in the seventh minute with a header which Manuel Neuer did well to push away from his goal.
As has often been the case this season, Bayern needed 45 minutes to get warmed up as they struggled to make any impression on the game.
They risked falling behind on the hour mark when Marcel Schafer ghosted in unmarked at the far post, but he was unable to guide his header inside the post with Manuel Neuer scampering across his goal.
Three minutes later, Bayern took the lead when a cross from left from Franck Ribery missed its intended recipient Mario Mandzkic, but was slotted inside the far post by Muller for his first goal in the Bundesliga this season.
Mandzukic could have made it two in the 80th minute, but first Naldo cleared his shot in front of the goal line before Diego Benaglio made a save from his second effort.
Bayern coach Pep Guardiola responded by sending an extra defender on with Jan Kirchhoff, but they still nearly conceded an equaliser as Naldo's header was saved at full stretch by Neuer, who preserved his side's win late on.