Having set a German league record last weekend with their eighth straight win since the start of the season, Bayern were left stunned as defender Jerome Boateng scored a late own goal to give Leverkusen the three points.
Despite the defeat, Bayern still enjoy a four-point lead at the top of the table, while Leverkusen are fifth.
"The defeat will not knock us of course, but we must learn the lessons from it," insisted Bayern coach Jupp Heynckes. "We have to maintain the same pace over the 90 minutes which we showed in the second-half."
The visitors took the lead when Leverkusen captain Simon Rolfes found Andre Schürrle on the wing, who threaded his pass through the Munich defence for striker Stefan Kießling to tap in on 42 minutes.
Bayern levelled on 77 minutes thanks to a header from striker Mario Mandzukic, but Leverkusen were not be denied their first win in Munich since October 1989.
Boateng managed to get his head in the way as Leverkusen's Sidney Sam headed towards goal, but the ball only flew into the top left-hand corner and past goalkeeper Manuel Neuer on 86 minutes.
There was also drama in Hannover as Borussia Mönchengladbach came from 2-0 down to score three goals in nine minutes to enjoy a 3-2 win and claim only
their third league victory of the season to go ninth with Hannover tenth.
Earlier, VfB Stuttgart striker Vedad Ibisevic headed a late winner to seal his team's 2-1 home victory over Eintracht Frankfurt.
Ex-Germany midfielder Christian Gentner played a big part in Stuttgart's win, which lifts them up to eighth, after he scored the opener in the sixth minute, then provided the final cross for Ibisevic's 84th-minute header.
Frankfurt equalised when captain Alexander Meier curled the ball inside the far post on 67 minutes before Bosnia and Herzegovina's Ibisevic hit his fifth goal of the season to leave Frankfurt third in the league.
On Saturday, defending champions Borussia Dortmund and Schalke had to dig deep as they returned to domestic action still in the glow of their midweek Champions League triumphs.
After Borussia shocked Real Madrid 2-1 in Dortmund on Wednesday, the same night Schalke enjoyed a 2-0 win at Arsenal, the pair both needed second-half goals to win their respective Bundesliga games.
Dortmund beat Freiburg 2-0 in heavy snow as centre-back Neven Subotic got the breakthrough the defending champions needed with a 54th-minute header.
Germany midfielder Mario Götze slotted home the second on 83 minutes to keep Dortmund fourth.
Schalke also had to labour for their three points in Gelsenkirchen as Peru striker Jefferson Farfan hit the only goal of the game against Nuremberg in the 77th-minute to put the Royal Blues second in the league.
VfL Wolfsburg, who parted company with coach Felix Magath on Thursday, picked up only their second win of the season with a 4-1 victory at 10-man Fortuna Düsseldorf to lift themselves off the bottom and up into 16th in the table.
Mainz are up to sixth after Hungary striker Adam Szalai scored a hat-trick against Hoffenheim. Having opened his account in the 21st minute, he doubled his team's tally with a second on 46 and wrapped up his hat-trick with a 64th-minute header to seal the 3-0 victory.