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.
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."
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.
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.
