The hosts led briefly through Hiroshi Kiyotake before Xabi Alonso restored parity with an excellent free-kick.
Muller put the champions ahead from the penalty spot in the 61st minute and headed home Arjen Robben's cross to seal the points.
Bayern's lead over Wolfsburg now stands at 11 points after their nearest rivals suffered a damaging maiden loss of 2015 at Augsburg.
Dominik Kohr scored the only goal after 63 minutes to bolster Augsburg's European ambition - they now lie fifth, level on points with fourth-placed Schalke, who were 3-1 winners at home to Hoffenheim.
Roberto Di Matteo's team were without a win for four matches in all competitions heading into the weekend, but Christian Fuchs settled their nerves with the opener.
Max Meyer then hit a brace before Kevin Volland registered a consolation for Hoffenheim, who are seventh with 10 games to play.
Jurgen Klopp's resurgent Borussia Dortmund were unable to make it five consecutive Bundesliga victories as they were held to a goalless draw away at Hamburg.
Franco Di Santo scored the winner for Werder Bremen, who increased Freiburg's relegation worries with a 1-0 win on the road.
Saturday's late kick-off produced a dramatic comeback from Mainz to earn a share of the spoils against Borussia Monchengladbach.
Lucien Favre's visitors were two goals to the good thanks to Raffael's double but Johannes Geis reduced the deficit and Shinji Okazaki headed in to ensure it ended 2-2.
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