Bayern, who have won only one league game in five this year but crushed Sporting 5-0 in Lisbon in the Champions League last week, are four points behind leaders Hertha Berlin, who went top with a 2-1 win over Borussia Moenchengladbach on Saturday.
Hamburg SV, leaders going into the weekend's matches, failed to regain top spot on Sunday when they lost 3-1 at home to VfL Wolfsburg and are a point behind Hertha.
Hoffenheim are third with 41 after a lacklustre 0-0 draw against Borussia Dortmund.
Wolfsburg, who displaced Bayern from fourth place, notched their fourth successive win after striker Grafite (pictured) opened the scoring with a penalty, awarded for a foul on Edin Dzeko, in the 12th minute.
Grafite scored again in the 25th when Marcel Schaefer raced past Hamburg's Guy Demel and cut into the middle for the Brazilian striker to net his 14th league goal.
"These two goals in the first half really broke our neck," Hamburg coach Martin Jol told reporters. "We did not lack passion but Wolfsburg were a more compact team and deservedly are high up in the table."
Striker Paolo Guerrero managed to pull one back for Hamburg with a low drive from 10 metres before Dzeko scored his 11th goal from close range just two minutes later.
BATTLING WERDER
Bayern, coming into the match on the back of an impressive performance in the away leg of their Champions League last-16 tie, failed to break down Werder's resistance even after the hosts were reduced to 10 men. Naldo was sent for fouling last man Bastian Schweinsteiger after 15 minutes.
"We have to accept the result as it is," said Bayern coach Juergen Klinsmann, who has yet to see his team at the top this season.
"We could have decided the match in our favour in the first half but after that we just did not get the necessary space," he told reporters.
With Bayern eager to make amends for a disappointing start to the year and Werder, pre-season favourites now lingering in mid-table despite ousting AC Milan in the UEFA Cup, both teams charged forward at a frantic pace.
Mesut Ozil almost grabbed the lead for the hosts after four minutes. Diego found the talented Germany international on the left inside the box where he did well to avoid one defender and shoot only for Ze Roberto to clear almost on the line.
Hamit Altintop came agonisingly close for Bayern minutes later but Werder keeper Christian Vander blocked the shot with Franck Ribery's rebound flying into the side netting.
Even the introduction of strikers Lukas Podolski and Landon Donovan for midfielders Schweinsteiger and Altintop in the second half failed to crack open a hard-working home defence.
VfB Stuttgart, seventh with 36 points, extended an unbeaten run dating back to November when goals by Elson and Sami Khedira gave them a 2-0 win at relegation candidates Karlsruhe.
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