After losing Daniel Schwaab to a controversial red card, Stuttgart then lost the game to a debatable penalty with Augsburg captain Paul Verhaegh netting the only goal of the game.
The win lifts Augsburg above Schalke into the top six, leaving Stuttgart with nine points from 12 games of the season and turning up the heat on their coach Armin Veh.
Hamburg moved above fellow-strugglers Werder Bremen thanks to a last-gasp 2-0 win in the 101st northern Germany derby.
Artjoms Rudnevs broke the deadlock with just seven minutes remaining before Raphael Wolf scored an own goal in stoppage time to seal Hamburg’s win.
Bremen ended the game with 10 men after Clemens Fritz was shown a second yellow card late on and dropped into the relegation zone as a result of the defeat at the HSV Arena.