Champions VfL Wolfsburg surged back from a goal down to beat Cologne 3-1 on Saturday to stay top of the Bundesliga after two matches.
Wolfsburg fell behind when Fabrice Ehret scored four minutes into the second half.
However, two goals in two minutes from Edin Dzeko and Pierre Wome (own goal) and a third by new signing Obafemi Martins three minutes from time gave the visitors six points from two games.
Cologne, with Lukas Podolski making his first home appearance after a three-year spell with Bayern Munich, had to survive intense pressure after Ehret put them ahead.
Striker Dzeko, though, equalised when he was left unmarked to slide in a cross on 73 minutes. Wome then headed in before Martins, signed from Newcastle United, combined well with Grafite to make it 3-1.
Bayern needed a second-half goal from the Bundesliga's most expensive signing Mario Gomez to salvage a 1-1 draw with Werder Bremen.
The visitors stunned Bayern six minutes before the break when Mesut Ozil converted a cross from Aaron Hunt.
Gomez, who joined from VfB Stuttgart in May for around €30m, rescued the home team 18 minutes from time when he beat keeper Tim Wiese to connect with a cross from the right by Philipp Lahm.
Bayern, who drew with Hoffenheim last week, have yet to win under new coach Louis van Gaal.
"I am not satisfied with the result but I am with my team," said the Dutchman. "We played outstanding for 30 minutes but failed to score (in that time)."
Ozil gave keeper Michael Rensing no chance when he notched his second goal in as many matches.
Bayern playmaker Franck Ribery came on after 62 minutes to make his first appearance of the season before Gomez levelled 10 minutes later.
Hamburg SV struck three times in the first 12 minutes on the way to a 4-1 drubbing of visiting Borussia Dortmund.
VfB Stuttgart eased past Freiburg 4-2, new signing Pavel Pogrebnyak hitting the opening goal and winning the penalty that led to the second.