The Bundesliga's leading scorer Stefan Kiessling took his league tally to nine this season when he levelled on 14 minutes after Bayern had taken an early lead through striker Mario Gomez.
Undefeated Leverkusen have 27 points from 13 matches, one ahead of Werder Bremen who demolished Freiburg 6-0 on Saturday.
Bayern, who have now drawn for the third consecutive match and have won only two of their last seven league games, are in seventh place on 21 points.
Fifth-placed Hamburg lost ground after a 1-0 home defeat by lowly VfL Bochum, who scored the winner on 77 minutes through Dennis Grote to leave the hosts in fifth place on 23 points.
"We played great football in the first half. I even expected that we would score to make it 2-1," Leverkusen coach Jupp Heynckes, who twice coached Bayern in the past, told reporters.
Bayern, still without injured playmaker Franck Ribery, winger Arjen Robben and striker Luca Toni, began strongly.
Coach Louis van Gaal, under mounting pressure given Bayern's mediocre season so far, gave a rare starting spot to Gomez and the German international quickly justified his selection.
A defensive blunder allowed Miroslav Klose to send Gomez into the box to slot home after eight minutes as Rene Adler rushed out of his goal.
CONSTANT THREAT
The celebrations among the majority of the 69,000 fans did not last long.
Kiessling chased down a long ball from Arturo Vidal, comfortably shook off defender Daniel van Buyten and fired past keeper Hans-Joerg Butt.
The gifted striker was a constant threat, exposing Bayern's chronic problem in central defence since the departure of Brazilian Lucio in the close season.
Bayern's Anatoliy Tymoshchuk should have done better a minute before the break when he was left unmarked in the box but only managed a weak shot that Adler had no trouble blocking.
Germany keeper Adler then made the save of the match with five minutes left when he denied Gomez from close range before the Bayern players left the pitch amid a chorus of jeers and whistles.
"We played without any confidence in the first half," said van Gaal, whose team could also be eliminated from the Champions League this week.
"It is sad because we really wanted those three points," the Dutchman told reporters.
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