Coach Pep Guardiola named a weakened team for the Bavarian derby and paid the price as Bayern were beaten for the first time in the German league since going down 2-1 at home to Bayer Leverkusen on October 28, 2012.
With one eye on Wednesday's Champions League clash at home to Manchester United, Guardiola started with three teenagers, giving Bundesliga debuts to wing-backs Ylli Sallahi and Mitchell Weiser while Pierre-Emile Hoejbjerg was named on the left wing.
The gamble backfired when Weiser lost possession to Augsburg's Daniel Baier who fed Sascha Moelders and the Augsburg striker blasted his shot past Bayern's goalkeeper Manuel Neuer with 31 minutes gone to claim the winning goal.
"Sooner or later we had to lose, we accept that and we have to prepare as quickly as possible for Manchester United," said head coach Guardiola.
"Next Wednesday is a final for us. It's a matter of life or death."
It was the third game in succession Bayern have fallen behind and Guardiola responded by bringing stars Mario Götze, David Alaba and Thomas Müller off the bench.
Left-back Alaba hit the post with 68 minutes gone as Bayern pushed in vain for the goal to keep alive hopes of becoming the first team to go through a Bundesliga campaign undefeated.
Having lost 4-2 at Borussia Dortmund in July's German Super Cup final and beaten 3-2 at home to Manchester City in the Champions League group stage last December, this was only Bayern's third defeat of the season since Guardiola took charge in June.
Bayern were already confirmed Bundesliga champions ten days ago when they wrapped up the title with a record seven games to spare and they remain 20 points clear in the table.
Later, second-placed Borussia Dortmund earned a morale-boosting 2-1 win at home to VfL Wolfsburg ahead of Tuesday's Champions League quarter-final, second-leg at home to Real Madrid.
After Croatia's Ivica Olic gave Wolves an early lead, a Robert Lewandowski header put Dortmund level before Germany winger Marco Reus hit the 77th-minute winner.
Borussia face a near-impossible task of overturning a 3-0 defeat from the first leg against Real to reach the Champions League's semi-finals.
"We showed an unbelievable mentality today," enthused Dortmund coach Jurgen Klopp.
"We made life hard for ourselves before the break, but it's often the case that you have to compensate for the missing punch with sheer willpower after a Champions League match.
"We changed our system and in the end we decided the match with our quality and pressure."
Schalke 04 are now three points adrift of Dortmund in third as they came from behind to claim a 1-1 draw at Werder Bremen.
Bremen took the lead when Argentina striker Franco di Santo netted after 15 minutes before Schalke teenager Leon Goretzka levelled on 33 minutes.
At the other end of the table, VfB Stuttgart improved their chances of avoiding relegation with a 2-0 win at home to Freiburg to escape the bottom three with goals by Romania's Alexandru Maxim and Austria's Martin Harnik.
Nuremberg drop into the bottom three after their 2-0 defeat at home to Borussia Mönchengladbach, who moved up to fourth and into the Champions League places at the expense of Bayer Leverkusen.
A first-half free-kick by Venezuela's Juan Arango and a late penalty from Max Kruse sealed the three points.
Earlier on Saturday, Leverkusen sacked coach Sami Hyypia in the wake of Friday's 2-1 defeat at strugglers Hamburg which left them with just one win in their last 11 games and facing a battle to qualify for next season's Champions League.
The 40-year-old former Liverpool captain, who took on his first senior coaching role last August, has been replaced by Sascha Lewandowski, the head coach of Leverkusen's junior side, who has five games to rescue their Champions League status.