Germany international Mueller, in sensational form this season, was left unmarked in the box to latch onto a superb Thiago Alcantara chip and tap in from close range in the 23rd minute for his ninth league goal as Bayern improved the record they had set themselves in the 2012/13 season.
Unbeaten Bayern, who did not need to hit top form and eased off late in the game granting Werder more space, have a maximum 27 points, seven more than second-placed Borussia Dortmund, who won 2-0 at Mainz 05 on Friday. Bayern face Arsenal in the Champions League on Tuesday.
"We won a very difficult game," said Bayern coach Pep Guardiola, whose team are chasing a record fourth consecutive Bundesliga title. "Werder were defending deep and they made it really hard for us."
"It was difficult finding spaces, especially because we did not have wingers. But I want to congratulate my team as this win means a lot to me", he told reporters.
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Bayern were missing half a dozen players, including injured wingers Franck Ribery, Arjen Robben and Kingsley Coman with Guardiola also resting winger Douglas Costa.
But they still dominated against Werder, who have now lost five consecutive Bundesliga matches.
The hosts had some efforts on goal and tested keeper Manuel Neuer but neither Anthony Ujah nor former Bayern striker Claudio Pizarro, who came on as a late substitute, could find the equaliser. The former German champions are stuck on seven points in 14th place.
Max Meyer scored a stoppage-time goal to give Schalke 04 a last-gasp 2-1 victory over 10-man Hertha Berlin and keep them firmly in third place on 19 points, one behind Dortmund.
Max Kruse scored a hat-trick as VfL Wolfsburg, who squandered a two-goal lead, beat Hoffenheim 4-2 in a rollercoaster game for their first win in four matches that lifted them to fourth on 15 points.
Borussia Moenchengladbach made it four wins in four league games under new coach Andre Schubert, crushing Eintracht Frankfurt 5-1 with two goals from Raffael and substitute Andre Hahn to continue their recovery after five consecutive defeats at the start of the season.
Gladbach, who travel to last season's finalists Juventus in the Champions League next week, now have 12 points and move up to 10th place.
Fellow Champions League club Bayer Leverkusen, who host AS Roma next week, drew 0-0 at Hamburg SV with keeper Rene Adler, surprisingly picked to start ahead of Jaroslav Drobny, ensuring a point for the hosts with some superb saves.
(Reporting by Karolos Grohmann, editing by Alan Baldwin and Martyn Herman)
