Dortmund, Schalke stumble in Bundesliga
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Kevin Schipplock's last-minute winning goal for Hoffenheim gave former Germany goalkeeper Tim Wiese his first win at the club since joining from Werder Bremen in the offseason.
Borussia Moenchengladbach drew 1-1 with Freiburg, Hannover beat Augsburg 2-0, and Timo Gebhart ended Nurnberg's six-game winless run with a 76th-minute diving header in his side's 1-0 victory over Wolfsburg.
Bayern, which lost to Bayer Leverkusen last weekend, is looking for its first win in Hamburg since 2006.
In Dortmund, Mats Hummels had a goal ruled offside and Marcel Schmelzer then shot narrowly wide as the home side started brightly.
Sebastian Kehl had to go off after 20 minutes after being caught in the face by Raphael Holzhauser's elbow. The Dortmund captain is a doubt for Tuesday's trip to Real Madrid in the Champions League.
Sven Ulreich pushed Hummels' next attempt onto the crossbar, and the defender's effort from the rebound was cleared off the line by a defender.
Dortmund striker Julian Schieber - who scored for Stuttgart when the sides last met in a spectacular 4-4 draw - was denied by former teammate Ulreich on the hour.
Vedad Ibisevic came closest for Stuttgart, only Roman Weidenfeller to block the Bosnian's shot, and there was still time for Robert Lewandowski to strike the crossbar at the other end.
Schalke remains second after only its second loss this season.
Kevin Volland fired Hoffenheim into an early lead before Roman Neustaedter equalized with a powerful header in the 37th minute.
Robert Firmino's penalty in the 67th made it 2-1 for Hoffenheim, only for Atsuto Uchida to equalize again with eight minutes remaining. Then Schipplock sprung the offside trap for Hoffenheim's first win in five games.
Lucien Favre was sent to the stands with six minutes remaining against Freiburg, after the Moenchengladbach coach reacted furiously to decisions against his team.
Igor de Camargo opened the scoring for `Gladbach in the 49th, but Daniel Caligiuri equalized from the penalty spot in the 77th.
In Hannover, Lars Stindl crossed for Mame Biram Diouf to score in the 26th, and the Senegal striker returned the favor for Stindl to curl a sweet shot inside the right post with five minutes remaining.