Dortmund's fourth loss in a row on the road in all competitions — including a 5-2 hammering at Real Madrid on Tuesday — left the team seven points off new Bundesliga leaders Leipzig.
The team's poor form has key players and sporting director Sebastian Kehl at a loss.
"I'm annoyed by the many goals we're conceding," Kehl said after Saturday's defeat. "We've been addressing this intensively but now we're standing here having to explain things that I can't explain."
Alexis Claude-Maurice made his first start since joining Augsburg in August and rewarded his new team with two goals from distance to turn the game around after Dortmund had led with an early Donyell Malen goal.
The game ended with 18-year-old Dortmund defender Almugera Kabar sent off for two yellow cards on his Bundesliga debut.
Leipzig look like two different teams, depending on which competition they're playing in.
In the Champions League, they've lost all three games but in the Bundesliga, Marco Rose's team now lead the standings — at least until Bayern Munich play on Sunday — and are unbeaten in eight matches.
On Saturday, they briefly looked like bringing their Champions League form to the Bundesliga before a second-half comeback to beat Freiburg 3-1.
Poor marking allowed Ritsu Doan to head Freiburg in front in the 15th — the first goal Leipzig have conceded in the Bundesliga since August 31.
But goals from defenders Willi Orban and Lutsharel Geertruida got Leipzig back into the game before Lois Openda scored from a tight angle to seal the win.
Late goals were key to Bayer Leverkusen's title win last season, but it went the other way as Romano Schmid's 90th-minute goal salvaged a 2-2 draw for Werder Bremen and dropped the champions five points off the pace.
Victor Boniface scored Leverkusen's opening goal, playing with his hand bandaged after a car crash which caused him to miss Wednesday's 1-1 Champions League draw at Brest.
Three of Leverkusen's last four games in all competitions have been draws.
El Bilal Toure scored a vital goal in Stuttgart's 1-0 win over Juventus on Tuesday in the Champions League, and the Mali forward did it again with a goal and assist to beat Holstein Kiel 2-1.
Toure surged for most of the length of the field on a counterattack to set up Deniz Undav for Stuttgart's first goal and scored the second with an audacious long-range shot.
That gave Stuttgart a much-needed first Bundesliga win in over a month, but only after surviving the last half-hour with 10 men after Jeff Chabot earned two yellow cards in the space of three minutes.
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