Han-Noah Massengo caused a stir when he scored the 2-1 goal for Augsburg with nine minutes left in regular time.
The loss was Bayern's first in the league since March 8 last year, when Bochum won 3-2.
For Augsburg, the surprising three points meant the club climbed to 13th place in the 18-team league table.
Bayern Munich lead the Bundesliga by eleven points, ahead of Dortmund, who play tonight.
National team midfielder Hugo Larsson came on after an hour of play, but it didn't help Eintracht Frankfurt, who lost 1-3 at home to Hoffenheim.
