The hosts, playing in front of a sellout 49,780 crowd, struck against the run of play when Croatian midfielder Ivo Ilicevic hammered a brilliant shot from 20 metres in the 36th minute.
A minute later Ilicevic, who was sent off near the end for a second caution, turned provider to set up countryman Srdan Lakic who slotted his third goal in two matches.
"Over 90 minutes we were the better team and had better chances but it was just not meant to be tonight," Bayern defender Philipp Lahm told reporters.
"A key moment was Mueller's chance. We survived that and then we played with a lot of heart," said Kaiserslautern coach Marco Kurz.
"We played well up until the final pass. Kaiserslautern though made space tight for us and had a lot of passion," said Bayern coach Louis van Gaal.
