Martin Harnik scored in the third minute to earn Stuttgart their first points since the winter break.
Defeat left the hosts third from bottom and 10 points from safety.
Nuremberg scored a last-gasp equaliser through substitute Sebastian Polter as they twice came from behind to earn a 2-2 draw at home to Hannover.
Szabolcs Huszti put Hannover in front in the 41st minute and Didier Konan put them back in front in the 68th minute after Timm Klose had levelled eight minutes into the second half.
But Polter, on the field since the 82nd minute, netted with almost the last kick of the match to ensure a share of the spoils.