Despite fighting for a draw, Bayern will leave frustrated after failing to turn overwhelming dominance into a win.
The game will forever be remembered for Robin Fellhauer's goal after just eight seconds - the fastest in Bundesliga history - which stemmed from a catastrophic error by Manuel Neuer.
Bayern controlled the ball with around 70% of the possession, created a mountain of chances - 29 shots to Augsburg's 12 - and generated a high expected goals total.
However, individual mistakes and a series of offside decisions cost them three points on the day. Harry Kane was the standout performer, providing both assists and striking the woodwork.
From the opening kick-off, the ball went back to Manuel Neuer, and the veteran goalkeeper took a heavy touch trying to chip the onrushing Fellhauer. The ball struck the Augsburg player, who raced clear and slotted into an empty net.
Bayern dominated territory and created chances, with Harry Kane hitting the crossbar, but Augsburg stayed organised and nearly doubled their lead when Chrislain Matsima skewed a close-range effort wide from a corner.
Luis Diaz thought he had levelled for Bayern in the 51st, but VAR disallowed the goal for offside. They found a goal four minutes later, though, as Kane delivered a precise pass for Saibari to finish smartly.
Against the run of play, Augsburg took back the lead in the 64th minute. Calvin Brackelmann's low shot from distance was parried by Neuer straight to Ribeiro, who tapped it home from close range.
Bayern two more goals ruled out for offside, including efforts from Serge Gnabry and Luis Diaz but they were able to find a late goal to share the spoils when substitute Nathaniel Brown finished from close range after good work involving Kane and Aleksandar Pavlovic down the left.
Union Berlin 1-0 SV Elversberg
A tight, low-scoring affair was decided late An der alten Forsterei. Livan Burcu scored the only goal of the game in the 81st minute to give Union a hard-fought home win.
Mainz 05 3-4 Bayer Leverkusen
Bayer Leverkusen triumph in a seven-goal thriller at MEWA Arena. The Visitors raced into a 2-0 lead inside nine minutes through Robert Andrich (5') and Patrik Schick (9').
Anthony Caci scored twice for Mainz (33' and 42') to level it at 2-2 by half-time.
Jarell Quansah (55') and Moussa Diaby (65') put Leverkusen 4-2 up, before Benedict Hollerbach pulled one back deep in stoppage time.
SC Paderborn 0-2 VfB Stuttgart
Stuttgart controlled the game at Home Deluxe Arena and claimed a solid away victory. Julian Chabot scored in the 25th minute, and Chris Führich sealed it in the 83rd minute.
TSG Hoffenheim 2-3 Hamburger SV
An end-to-end contest at PreZero Arena concluded with a late twist.
Yussuf Poulsen gave HSV an early lead in the 12th minute before Hoffenheim equalised through a Sebastiaan Bornauw own goal on the stroke of half-time.
The hosts took the lead through Bambase Conte in the 53rd minute but were put on the back foot in the 65th minute when Bernardo was shown a his second yellow card.
They held on to the closing stages, but Terem Moffi equalised for Hamburg in the 83rd minute, and Miro Muheim then scored a dramatic winner four minutes into stoppage time.
RB Leipzig 6-0 Eintracht Frankfurt
Christopher Nkunku's first-half hat-trick highlighted a dominant home performance at the Red Bull Arena.
Ezechiel Banzuzi scored inside the first minute, Nkunku made it 2-0 in the 5th minute, then completed his treble with goals in the 41st and 44th minutes to make it 4-0 at half-time.
Antonio Nusa added a fifth in the 54th minute, and Tidiam Gomis finished the rout in the 89th minute. Frankfurt were overrun, continuing their defensive struggles so far this season.