The German champions were headed for a win until Muller turned the ball into his own net in the 36th minute to help Leverkusen secure a share of the spoils from the Allianz Arena.
Defender Niklas Süle, who will be joining title rivals Borussia Dortmund next season, scored the opener for Bayern at the Allianz Arena after Leverkusen failed to clear a corner.
Bayern continued to attack but we’re toothless in the final third, with key man Robert Lewandowski scuffing a few chances to double the lead for the Bundesliga table toppers.
Nine minutes from half time, Muller, unchallenged, diverted a freekick from Leverkusen’s Kerem Demirbay into his own net.
Sven Ulreich, deputising for Manuel Neuer in goal for Bayern, had to pull out all the stops to help Bayern leave the game with their dignity intact, or it would have been worse for the champions.
Bayern went on to have 18 shots in the game and Leverkusen only managed nine, but “the Eternal Bridesmaids” held on to become only the third club to take points off Bayern at the Allianz Arena this season.
The draw was the second game in which Bayern dropped points in four games, after the 1-1 draw with Red Bull Salzburg in the first leg of their UEFA Champions League round of 16 tie.
Bayern remain at the top of the standings, nine points clear of second-placed Borussia Dortmund, who have a game in hand.
Leverkusen, meanwhile, are third, 14 points behind Bayern.
Bayern lacked punch, Nagelsmann says
Bayern coach Julian Nagelsmann said that his side had a few shortcomings in his post match comments to Sky Sports Germany.
“The first half hour was very good from us. We were in good control during that spell. Then we conceded an avoidable goal. After that, we were lucky not to concede a second goal,” he said.
“We made too many simple mistakes … we lacked a bit of punch but the point is fine for both teams. Thomas Müller is not happy, but not mega dejected either. It happens to the best, it won’t knock him out permanently.”
Goal scorer Niklas Süle also commented on his team’s performance in the draw.
“After the unfortunate 1-1 we fell apart a bit,” Süle told Sky Sports after the game. “That mustn’t happen to us. You have phases in which you have a little less self-confidence when setbacks come. The 1-1 is too little.”
Leverkusen’s manager gave his team a glowing review after the game.
“It took us a while to get used to the new system but it was also due to Bayern’s performance,” said Seoane. “Then we gained confidence and had some very good situations. Compliments to the team, they fought with solidarity and were very willing to suffer.”
Bayern will hope to pick the scraps up on Tuesday as they face RB Salzburg in the second leg of their Champions League round of 16 tie.