Schalke stays hot against Hannover
Jefferson Farfan opened the scoring in the 39th, converting from close range after Sead Kolasinac outran Hannover defender Marcelo on the left.
Farfan instigated Schalke's second goal five minutes later, playing through a brilliant ball for Atsuto Uchida, who cut back for Klaas Jan Huntelaar and he in turn left it for the better positioned Max Meyer to stroke home.
Huntelaar headed over early in the second half and Meyer drew a good stop from Hannover `keeper Ron-Robert Zieler as the home side came closest to adding to the scoreline.
The visitors opened the scoring against the run of play in the 35th minute through Arkadiusz Milik and built on the lead when Halil Altintop sprung the offside trap for Andre Hahn to finish with aplomb in the 44th.
Stuttgart's hopes effectively evaporated with Vedad Ibisevic's sending off in the 53rd. TV replays showed the Bosnian striker struck out at Jan-Ingwer Callsen-Bracker's face in an off-the-ball incident, leading the Augsburg defender to fall to the ground.
Hahn scored his second of the game three minutes later for his ninth of the season. Konstantin Rausch pulled one back for Stuttgart in the 62nd, but Tobias Werner ended any hopes of an unlikely comeback two minutes later.
Augsburg stretched its unbeaten run to eight league games and climbed to eighth, while Stuttgart is just two points off the relegation zone after its seventh defeat in eight games.
''It's a difficult period. There were many negative highlights for us today,'' Stuttgart sports director Fredi Bobic said. ''The first goal was the turning point. We had them under control for 30 minutes before that.''