The Bavarians, who have lost just once all season, needed only a point to clinch the crown after nearest challengers Borussia Dortmund suffered a defeat at Hoffenheim on Saturday night.
But Stuttgart, chasing a place in next season’s Champions League, threatened to spoil the party when Chris Fuhrich curled home a superb effort after 21 minutes.
The hosts responded through Raphael Guerreiro 10 minutes later, before on-loan Chelsea forward Nicolas Jackson – deputising for Harry Kane – put them ahead two minutes after that.
Alphonso Davies added a third nine minutes before the break, improvising well to flick the ball past Alexander Nubel from inside the area after a pass from Luis Diaz.
Coming on to replace Jamal Musiala at half-time, it took Kane seven minutes to add a fourth with his 32nd league goal of the season. while Chema Andres scored a late consolation for the visitors in the 88th minute.
The victory seals a 13th Bundesliga title in the past 14 seasons for Bayern and keeps their hopes of winning the treble alive, with semi-finals against Bayer Leverkusen in DFB‑Pokal and Paris St-Germain in the Champions League to come later this month.
