Bayern Munich opened up an eight-point lead at the Bundesliga summit as their 1-0 win over Hannover coincided with Borussia Dortmund suffering a 2-1 defeat at Cologne.
Reports linking Pep Guardiola with a move away from the Bavarian side when his contract expires at the end of the season have intensified in the past week, and his team would have fallen behind at the HDI Arena had Manuel Neuer not got enough on Leon Andreasen's header to divert it onto the crossbar.
Ron-Robert Zieler continued an impressive first half in which he denied Thiago Alcantara, Kingsley Coman and Muller to keep Robert Lewandowski at bay after the interval.
Michael Frontzeck's team never looked like mounting a comeback and Dortmund's late collapse means Bayern head into the winter break with a sizeable advantage.
The trip to Cologne started brightly for Thomas Tuchel's side when Sokratis Papastathopoulos steered them into an 18th-minute lead.
Peter Stoger's responded positively and Frederik Sorensen was denied by Roman Burki before Yannick Gerhardt hit the post.
Maximilian Arnold put Dieter Hecking's team in front, but Daniel Didavi - whose first goal was a sensational effort from 25 yards - scored either side of Filip Kostic's strike as the strugglers came from behind to get their first Bundesliga win under Jurgen Kramny.
Jan Moravek's second-half strike saw Augsburg make it five top-flight games without defeat with a 1-0 win away at Hamburg.
