Schalke, Eintracht Frankfurt and Bayer Leverkusen all won in the Bundesliga while Borussia Dortmund drew at RB Leipzig.
Michy Batshuayi continued his good start to life with Borussia Dortmund as he scored again in a 2-0 win over Hamburg.
Goalkeeper Rene Adler had a night to forget as he was involved in two howlers during Mainz's DFB Cup exit to Eintracht Frankfurt.
Schalke and Frankfurt reached the semi-finals of the German Cup after wins over Wolfsburg and Mainz respectively.
Ademola Lookman scored a dramatic late winner on his debut for RB Leipzig in a 1-0 victory at Borussia Monchengladbach in the day's late game.
In-form Bayer Leverkusen climbed to second in the Bundesliga following a 2-0 win at home to Mainz.
Naby Keita set RB Leipzig on their way to a 3-1 win over Schalke on Saturday evening.
Sven Ulreich saved Chadrac Akolo's 95th-minute penalty as Bayern Munich ground out a hard-fought 1-0 win at Stuttgart.
RB Leipzig missed the chance to close on Bundesliga leaders Bayern Munich after they were held to a 1-1 draw at Wolfsburg.
Bayern Munich moved eight points clear at the top of the Bundesliga after a 1-0 victory at Eintracht Frankfurt on Saturday.
Bayern Munich strengthened their grip on the Bundesliga title race with a 3-0 win over Augsburg.
Bayern Munich moved six points clear of Borussia Dortmund in the Bundesliga table with a 3-1 victory in Der Klassiker at Signal Iduna Park.
Jupp Heynckes enjoyed a 5-0 victory over Freiburg on his return to Bayern Munich, while Borussia Dortmund lost to RB Leipzig.
Borussia Dortmund continued their impressive start to the season as they secured a fourth straight win, seeing off Augsburg 2-1.
Borussia Dortmund powered two points clear at the top of the Bundesliga with a thumping 6-1 win over Borussia Monchengladbach.
Borussia Dortmund leapfrogged Bayern Munich back into top spot in the Bundesliga following a 3-0 win at Hamburg.
Naby Keita was sent off in Leipzig's 2-2 draw with Monchengladbach while Robert Lewandowski scored two for Bayern Munich against Mainz.
Mark Uth netted twice as defending champions Bayern Munich slumped to a shock 2-0 defeat at Hoffenheim on Saturday.
Marko Arnautovic scored his first West Ham goal in a 2-2 draw with Werder Bremen, while Leicester lost at Wolves and Stoke beat Bolton.
Middlesbrough forward Viktor Fischer has joined Mainz, the Bundesliga club have announced.
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