Stuttgart took the lead through Tanguy Coulibaly before Bundesliga champions Bayern Munich roared back to seal all three points.
Bayern Munich returned to winning ways in the Bundesliga as goals from Kingsley Coman, Robert Lewandowski and Douglas Costa sealed a 3-1 victory over Stuttgart on Saturday.
The champions were held to a 1-1 draw by Werder Bremen last weekend and although normal service was resumed at the Mercedes-Benz Arena, they did not have it all their own way against Pellegrino Matarazzo's side.
Stuttgart could easily have added to Tanguy Coulibaly's opener midway through the first half but Hansi Flick's men powered back to claim maximum points through fine strikes from Coman and Lewandowski before the break and a late third from Douglas.
The result means Bayern have won 26 of their last 29 top-flight games and helped them open a two-point lead at the Bundesliga summit after Borussia Dortmund dropped points at home to Cologne.