Gnabry scored both facet of 1/2-time earlier than the flood gates opened with 3 goals in a devastating best-minute spell as Lewandowski scored in brief succession.
The Poland striker has now scored 18 desires in 16 league video games this season as Bayern earned a tenth directly Bundesliga win at Stuttgart dating returned to 2009.
The Bavarian giants remain on course to win a tenth consecutive Bundesliga title, but 2d-located Borussia Dortmund can trim their gapping lead after they host bottom side Greuther Fuerth on Wednesday.
Injuries and illness already supposed Bayern once more fielded Jamal Musiala, 18, out of function within the shielding midfield along Marc Roca and winger Kingsley Coman went off with a leg knock in the opening 1/2 hour.
Coman's replacement Leroy Sane installation Gnabry's establishing goal by way of charging via an gaping hollow, which grew wider when Stuttgart centre-returned Waldemar Anton misplaced his footing.
Sane squared to Stuttgart-born Gnabry who curled his shot round home goalkeeper Florian Mueller to make it 1-zero on the damage.
Stuttgart raised the pace on the begin of the second one half as strikers Philipp Foerster and Omar Marmoush both had possibilities, however it was genuinely one-way site visitors from Bayern thereafter.
The visitors doubled their lead whilst Marmoush yielded possession and the ball turned into moved to Gnabry who once more curled his shot around the diving Mueller.
Stuttgart's defence capitulated as Bayern scored 3 dreams in 5 devastating mins.
