
At Gottlieb-Daimler Stadion, Mario Gomez put Stuttgart ahead after seven minutes with his stomach after Ludovic Magnin's cross evaded keeper Oliver Kahn.
Yildiray Basturk doubled the lead in the 30th minute after firing a splendid shot into the top corner of the net.
Gomez made it 3-0 three minutes before the break, notching home from close-range to finish off series of passes in Bayern's area.
Luca Toni scored on the rebound four minutes from time to notch a consolation for the visitors.
Elsewhere, Mohamed Zidan's Hamburg drew 1-1 with Schalke away.
Mladen Krstajic fired the hosts in front in the 12th minute before Ivica Olic leveled the score 10 minutes before the break.
The Egyptian forward did not take part in the game due to injury.
Bayern are still on top of the league table with 28 points, one ahead of second-placed Werder Bremen, who crushed Karlsruhe 4-0.
Hamburg are also one point behind Bayern but they sit third due to their inferior goal difference to Bremen.
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