Bayern took the lead against the run of play with a fine 67th-minute shot from Toni Kroos and seven minutes later Mario Goetze slotted in the equaliser for the visitors from a Marco Reus corner.
Dortmund had keeper Roman Weidenfeller to thank for a string of superb saves in the closing stages.
Bayern, who ended a five-game losing streak against Dortmund, have 38 points, 11 ahead of the champions who remain third.
Defender Holger Badstuber tore cruciate ligaments in his right knee and will be sidelined for Bayern for several months.
Second-placed Bayer Leverkusen have 30 points after a 1-0 victory over Nuremberg.
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