Dortmund remain six points behind league leaders Bayern, who also bounced back from a disappointing week with a 4-1 win over bottom club Greuther Fuerth.
Bayern, who lost at promoted Bochum last weekend, came from behind to beat Fuerth thanks to a second-half brace from Robert Lewandowski.
"This was an important win for us, psychologically and in terms of the table," Bayern coach Julian Nagelsmann told DAZN.
Fuerth striker Jamie Leweling was twice denied by Sven Ulreich after breaking free of the Bayern back line, before Branimir Hrgota gave his side the lead with a deflected free-kick shortly before half-time.
Having lost Corentin Tolisso to injury midway through the first half, Bayern appeared to be facing yet another miserable afternoon.
But the champions bounced back just seconds after the restart, Lewandowski bundling the ball over the line from close range after a sharp run down the right from Serge Gnabry. They took the lead just after the hour when Sebastian Griesbeck turned a Thomas Mueller cross into his own net to score an own goal against Bayern for the second time this season. Fuerth refused to roll over, with Max Christiansen and Marco Meyerhoefer both hitting the post a few minutes later.
Lewandowski ended the resistance 10 minutes from time, nodding the ball in from close range after Niklas Suele had set him up with a pinpoint header across the face of goal.
Eric-Maxim Choupo-Moting completed the comeback with a tap-in in injury time.
In Sunday's late game, RB Leipzig reclaimed fourth place with an impressive 6-1 win at Hertha Berlin.
Leipzig took the lead on 20 minutes when Linus Gechter deflected in Benjamin Henrichs' shot.
Struggling Hertha hit back on the counter-attack just after half time, Stevan Jovetic picking out the bottom corner.
Marc Kempf was sent off after bringing down Christopher Nkunku in the box, and the Frenchman restored Leipzig's lead with the resulting penalty.
Nkunku and Dani Olmo added two more in the following 10 minutes as 10-man Hertha wilted.
Amadou Haidara rubbed salt in the wound ten minutes from time with a blistering long-range shot into the bottom corner, before Yussuf Poulsen added a sixth with a delicate chip over the goalkeeper.
