Neither side created much across an even first 15 minutes, with half-chances squandered by Kim Min-Jae and Bilal El Khannouss at either end. However, the contest stepped up a gear on 21 minutes, as El Khannouss rolled a pass behind Josip Stanišić and Chris Führich curled home his fifth league goal of the campaign from a tight angle.
That briefly looked like upsetting Bayern’s big day, but the champions hit back in style, with three goals in six minutes just after the half-hour mark.
Jamal Musiala bundled past two Stuttgart challenges down the hosts left flank, before his cutback was stabbed home from close range by Raphael Guerreiro, and a Stuttgart error on the halfway line just seconds later released Luis Díaz to tee up Nicolas Jackson for a tap-in.
With the tide of the game turned, Vincent Kompany’s side were relentless before the break, as Alphonso Davies’ deflected 15-yard strike flew past Alexander Nubel for his first goal of the season, to effectively wrap up the result - and Bayern’s title defence - all before the break.
Kompany opted to introduce Harry Kane and Michael Olise from the Bayern bench at the start of the second half, and the former kept the momentum going just seven minutes after the restart, tucking home his 32nd league goal of the campaign. That strike threatened the possibility of a procession in the closing stages, but Nübel superbly denied Leon Goretzka on the hour as Kompany’s charges eventually took their foot off the gas.
Stuttgart at least netted a late consolation through Chema Andres, whose sweet strike from the edge of the area proved too strong for Jonas Urbig.
The title was long since secure, however, and Bayern's focus now switches to the DFB-Pokal and the UEFA Champions League with a treble still on the table.
Visitors, Stuttgart retain a two-point lead over Hoffenheim in the race for UCL qualification, but have now lost four of their last seven matches in all competitions.
Flashscore Man of the Match: Luis Diaz (Bayern Munich)