Dortmund substitute Paco Alcacer completed a hattrick with the last kick of the game for a 4-3 win over Augsburg.
Bayern Munich slumped to another defeat in the Bundesliga as Borussia Moenchengladbach pounded the defending champion 3-0 on Saturday.
Meanwhile, Borussia Dortmund maintained their unbeaten start in dramatic fashion.
Bayern, beaten by Hertha Berlin last weekend, were bidding to end a three-game run without a win, but the latest loss will pile the pressure on Niko Kovac and call into question his ongoing tenure as coach.
"We're making too many individual mistakes and these are causing uncertainty in the team," Kovac said.
Bayern started the season with seven wins across all competitions but have dropped to fifth after seven rounds of the league, four points behind Dortmund.
'Gladbach striker Alassane Plea capped a fine team move by eluding Niklas Suele and curling his shot from distance beyond Manuel Neuer inside the far post in the 10th.
Just six minutes later, Lars Stindl left Mats Hummels standing and made it 2-0. Jonas Hofmann played the final pass for both goals.
Kovac brought on Franck Ribery and Serge Gnabry in a bid to shake a response from his side at the break, but 'Gladbach maintained their grip of the game.
Robert Lewandowski had a goal ruled out for offside, and Patrick Herrmann rubbed salt in Bayern's wounds when he scored the third with minutes to play.
DORTMUND DRAMA
Dortmund substitute Paco Alcacer completed a hattrick with the last kick of the game for a 4-3 win over Augsburg.
The Spanish striker twice drew Dortmund level before Mario Goetze, another substitute, scored on his first league appearance of the season to make it 3-2 to Dortmund in the 84th minute.
Dortmund fans were already celebrating what they thought was another comeback win - the side came from two goals down to beat Bayer Leverkusen 4-2 last weekend - when Michael Gregoritsch replied for the visitors with a header from a corner for 3-3.
Dortmund's final chance came after Sergio Cordova conceded a free kick for a brutal foul on Achraf Hakimi. Alcacer fired the set-piece over the Augsburg wall in the sixth minute of injury time.
"It's fantastic, for the spectators, but also for us, because anything was possible - counterattacks, goals," an emotional Dortmund coach Lucien Favre said.
"With this support behind us, the team has belief, it's clear, but we always try to play, even if there are some things to be corrected, especially in defense."
The win kept Favre's side top of the league going into the international break.
The Swiss coach singled out Alcacer for praise.
"A very, very, very good transfer," Favre said of the summer signing from Barcelona.
Alcacer has six goals in three league appearances, all of them as a substitute.
AMERICAN GOALSCORERS
United States internationals Weston McKennie and Bobby Wood helped their sides to wins.
McKennie followed up his first goal in the Champions League on Wednesday with his first in the Bundesliga to set Schalke on its way to beating promoted Fortuna Duesseldorf 2-0.
It was Schalke's third win in a week including the victory over Lokomotiv Moscow after it started the league with five defeats.
Wood scored twice in the first half to help Hannover climb off the bottom with a 3-1 win over Stuttgart.
Wood, who hadn't scored for the club since his summer switch from relegated Hamburger SV, scored both with his head off crosses from Miiko Albornoz.
Also, Mainz held Hertha Berlin to 0-0.
