Bayern coach Pep Guardiola fielded an experimental side, in view of the second leg of his side's Champions League quarter-final against Manchester United on Wednesday, and a Sascha Molders goal in the first half punished them.
Augsburg were good value for the win against a sub-standard Bayern and boosted their chances of qualifying for Europe next season in the process.
Guardiola came good on his promise to rotate his team, fielding Mitchell Weiser, Pierre Emile Hojbjerg and Ylli Sallahi in his starting XI, with Arjen Robben and Franch Ribery not even named in the matchday squad.
That evened the playing field somewhat and Augsburg sensed their opportunity, attacking from the outset.
Midway through the first half they had their first big chance to take the lead, when Alexander Esswein's low cross was missed by Molders but not by Halil Altintop, who was denied by Manuel Neuer in a one-on-one situation.
Five minutes later, the hosts took the lead when Weiser got caught in possession by former 1860 Munich midfielder Daniel Baier, who threaded a pass through for Molders.
Faced with only Neuer to beat, the Augsburg striker got his head down and chose power over precision to beat the Germany number one.
Bayern were stronger in the second half, but Wednesday's game against United was clearly in the back of their minds and preventing them from going the extra mile.
Javi Martinez sent a header wide before Augsburg nearly doubled their lead when they cut through the Bayern defence once again, with Esswein this time faced with only Neuer to beat but unable to follow Molders' example as the keeper made a fine save with his arm.
Bayern increased the pressure as the clock ticked down, keen to defend their proud unbeaten Bundesliga record, even without their first-choice team.
Mario Gotze and Thomas Muller both came on, but were unable to alter the course of the game as Augsburg held on for a historic win.