Bayern were on the attack for long periods, but Werder goalkeeper Christian Vander put in an inspired performance to keep a clean sheet.
It had been end-to-end stuff from the beginning, but the match changed when Werder defender Naldo was sent off after 15 minutes for a professional foul on Bayern midfielder Bastian Schweinsteiger.
The visitors created several good opportunities afterwards, with former Werder player Tim Borowski going close on four first-half occasions.
Bayern coach Juergen Klinsmann brought on Lukas Podolski for Schweinsteiger at half-time, but the visitors could not turn their dominance into goals.
Also on Sunday, Wolfsburg ended Hamburger's proud home run with a 3-1 away victory. Hamburg thus suffered their first home defeat of the season as the "Wolves" extended their winning run to four straight matches.
Karlsruher was dealt another blow in their quest for Bundesliga survival by losing to South-West rivals Stuttgart 0-2 at home.
The defeat leaves Karlsruher, who have failed to score in their last three games, in 17th place
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