Dortmund's woes continue with German Cup exit at Wolfsburg
Scoreless after 90 minutes, the match looked set for penalties before Jonas Wind tapped in from close range in the 117th minute.
Dortmund and new coach Nuri Sahin came into the match under pressure, last season's Champions League finalists sitting seven points off top spot in the league after just eight games.
Dortmund had lost their last four matches away from home in all competitions but had the best of the opening half, Maximilian Beier hitting the post with just the goalkeeper to beat.
The visitors dominated possession but lacked fluency in attack and failed to break through and looked to have set their sights on penalties as extra time ran down.
Wind however scored for the hosts with three minutes remaining, heaping more pressure on Sahin and his struggling side.
"Extremely bitter to concede a goal like that after 120 minutes. It's tough," said Dortmund's Pascal Gross.
"We've got injury problems, but that's no excuse - we had chances to score."
Stuttgart won 2-1 at home to eliminate last year's finalists Kaiserslautern thanks to goals from Nick Woltemade and Chris Fuehrich.
Woltemade put Stuttgart in front after 14 minutes but Kaiserslautern levelled things up from the spot through Boris Tomiak late in the first half.
Ermedin Demirovic, who laid on the opener, was the provider again, setting up Fuehrich as Stuttgart re-took the lead with 15 minutes remaining.
Earlier on Tuesday, a brace from Patrik Schick put German Cup holders Bayer Leverkusen on course for a 3-0 victory over Elversberg.
Leverkusen burst out of the blocks, Schick scoring twice in the opening 10 minutes. Aleix Garcia added a third with a stunning free-kick on the 36-minute mark.
Elversberg beat Leverkusen in the first round of the 2022-23 German Cup, making them the last team to beat the current holders in the competition.
Leverkusen coach Xabi Alonso praised the "intelligent" Schick and said: "What's most important is that we made it to the next round."
RB Leipzig, who won back-to-back German Cups before Leverkusen's triumph, beat St Pauli 4-2 at home, with Yussuf Poulsen scoring a brace.
The hosts were 2-0 up after 17 minutes thanks to goals from Poulsen and Christoph Baumgartner. Morgan Guilavogui grabbed one back on 28 minutes but Poulsen added another two minutes later.
St Pauli's Swedish defender Eric Smith scored early in the second half but Norwegian forward Antonio Nusa put the match to bed with a classy solo goal with 10 minutes remaining.
Elsewhere, goals for Alexis Claude-Maurice, Arne Maier and Samuel Essende took Augsburg past five-time champions Schalke with a 3-0 win.
Karlsruhe beat Kickers Offenbach 2-0, Cologne beat Holstein Kiel and Regensburg eliminated Greuther Fuerth.
On Wednesday, 20-time champions Bayern Munich travel to Mainz while Eintracht Frankfurt host Borussia Moenchengladbach.
