Bayern was beaten 2-1 at home by Hoffenheim on Saturday.
"I'm annoyed that we couldn't build on the euphoria, the good vibes today," Bayern coach Niko Kovac said.
Sargis Adamyan scored twice to seal the first-ever victory at Bayern for the visitors, who also won away for the first time this season.
"I'm very proud of my team," Hoffenheim coach Alfred Schreuder said.
Schalke failed to take advantage of Bayern's slip-up as Cologne defender Jonas Hector scored in injury time to grab a 1-1 draw, ending Schalke's four-game winning streak and denying it top spot in the league.
Borussia Dortmund was held to a third consecutive 2-2 draw in the league at Freiburg, while Leipzig and Bayer Leverkusen drew 1-1. Also, Mainz won 2-1 at relegation rival Paderborn.
BAYERN BEATEN
Serge Gnabry, who scored four times at Tottenham, had an early goal ruled out against Hoffenheim as Joshua Kimmich strayed offside.
Robert Lewandowski then sent Gnabry on his way with his heel, but Hoffenheim goalkeeper Oliver Baumann saved his shot and Corentin Tolisso's effort from the rebound. Tolisso's next effort was just over.
Lewandowski had a penalty appeal waved away before the interval after he went down under Kevin Akpoguma's challenge.
Bayern displayed little urgency after the break and was shocked when Adamyan fired the visitors in front in the 54th minute. Sebastian Rudy played in Dennis Geiger, who found Adamyan and he shot home through Jerome Boateng's legs.
The visitors almost scored again through Stefan Posch in the 65th before Lewandowski equalized with a header from substitute Thomas Müller's cross in the 73rd.
It was the Poland striker's 11th goal in seven Bundesliga games.
But Adamyan scored again six minutes later, again shooting through Boateng's legs and into the bottom corner, to put the brakes on Bayern's Oktoberfest celebrations.
SCHALKE DENIED
Suat Serdar headed Schalke into a 71st-minute lead, putting his team on course for its fifth straight win. That would have been enough to lead the Bundesliga for the first time since March 2010.
But Hector's late header from a corner earned Cologne a point and left five teams — Bayern, Freiburg, Leipzig, Schalke, Leverkusen — level on 14 points at the top.
After seven games, Bayern leads on goal difference.
Borussia Mönchengladbach and Wolfsburg have a chance to grab the lead by winning their respective games on Sunday. Gladbach plays Augsburg and Wolfsburg hosts Union Berlin.