The two Germany internationals struck in either half to condemn the Swabians to defeat, who were overtaken by Leverkusen in fifth place in the Bundesliga standings
Mario Gomez struck in the first half before Thomas Muller fired home at the death to seal all three points for the Bavarians, who are already assured of a second place finish in the league.
The match was certainly not one for the purists, with both teams struggling to get into any kind of rhythm with the end of season clearly in sight.
Stuttgart will fell like they should have came away with something more though, having hit the woodwork twice, and now see Bayer Leverkusen leapfrog them by a point into fifth place, though both teams are still guaranteed Europa League football next season.
After a punishing 120 minutes against Real Madrid on Wednesday, Bayern coach Jupp Heynckes opted to rest many of his first-teamers, making eight changes from the XI that started at Santiago Bernabeu.
It was a familiar face at the end of the first chance of the match after four minutes though, as Gomez, one of only three survivors from midweek, created space at the top of the box before firing just over the bar.
Stuttgart were quickly back down the pitch, and should have been ahead when Georg Niedermeier’s planted a close-range header onto the crossbar.
However, both teams failed to really build on the promising start, and were in no hurry to force the issue in the final third, with the match having something of an end-of-season feel to it.
It was not the biggest surprise, then, that a mistake provided the platform for the opening goal just after half an hour.
Francisco Rodriguez’s calamitous attempt at a clearing header instead let Muller through on goal, who squared to Gomez to tap in from a few yards out.
Holger Badstuber almost put Stuttgart back on level terms within moments of the restart with an inadvertent back-pass that Hans-Jorg Butt was forced to claw away from danger.
Soon after, Tamas Hajnal’s cross was headed onto the woodwork by Shinji Okazaki from which Christian Gentner, with the goal at his mercy, nodded over.
Ivica Olic teed up David Alaba at the edge of the box four minutes after half-time, but the full-back’s shot flashed narrowly off target.
But much like the first half, both teams seemed to be lacking a cutting edge, with the tempo of the game falling well short of inspiring.
Substitute Arjen Robben saw a late shot saved by Sven Ulreich, with Muller also thwarted on the goal-line by Gotoku Sakai from the rebound.
Muller would have the final say in injury time though, stroking home a cutback from Olic to put the result beyond doubt at the Allianz Arena.
In the final round of Bundesliga matches to come, Bayern visit Koln while Stuttgart play host to Wolfsburg.