Goals from Mats Hummels in the 12th minute and Robert Lewandowski after the break looked set to get Bayern back on track after last week's 2-2 home draw with VfL Wolfsburg and Champions League rout in Paris on Wednesday.
Yet Hertha needed just five minutes in the second half to level through goals by Ondrej Duda, after a sensational solo run past four players from Genki Haraguchi, and Salomon Kalou.
The result left Bayern, who fired Italian Ancelotti a day after their 3-0 Champions League group stage loss at Paris St Germain, in second place on 14 points, five off leaders Borussia Dortmund who beat Augsburg 2-1 on Saturday.
Hoffenheim are behind Bayern on goal difference after losing 3-2 at Freiburg on Sunday to end their unbeaten run this season.
RB Leipzig, last season's runners-up, scored a goal in each half through Lukas Klostermann and Yussuf Poulsen to beat bottom club Cologne 2-1 and move up to fourth on 13.
The change in coaches this week did nothing to stop Bayern's dip in form and, despite a dominant first half, they gave Hertha too much space to come back after the break.
The Berliners had little trouble getting through a struggling Bayern backline that has already conceded seven goals this season, as many goals as 17th-placed Werder Bremen.
"We had a lot of chances and scored just twice. It is disappointing because we should have been more efficient," Sagnol told reporters.
"Without concentration we are not the best team in Germany. "It is not just the defence, it is a team problem. We have to act collectively to find the right balance again."
There was more bad news for Bayern with winger Franck Ribery taken off injured after he turned his left knee.
"Franck is in serious pain. We hope it is nothing bad but it does not look good," said Bayern sports director Hasan Salihamidzic.
(Reporting by Karolos Grohmann; Editing by Toby Davis and Ken Ferris)
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