The hosts, who had only won twice in the league this season coming into the match, went 2-0 up in the first half via Mads Pedersen in the 23rd minute and a 35th-minute Andre Hahn header.
Robert Lewandowski replied in the 38th minute but Julian Nagelsmann’s team could could not rescue themselves as they dropped points for only the third time this term.
The champions remain four points clear of second-placed Borussia Dortmund, who host Stuttgart on Saturday.
Augsburg move up from 16th to 15th, swapping places in the table with Stuttgart.
In Ligue 1, title-holders Lille were held to a 2-2 draw at Monaco.
Lille’s Jonathan David scored a penalty in the fifth minute and struck again in the ninth, before Krepin Diatta pulled a goal back just prior to the interval.
Monaco then had Strahinja Pavlovic sent off in the 78th minute, but were level five minutes later thanks to a volley by Wissam Ben Yedder. Monaco are up to seventh, while Lille stay 12th.
In LaLiga, second-bottom Levante remain winless but picked up a point after battling out a 0-0 draw with Athletic Bilbao at Estadi Ciutat de Valencia.