The visitors weathered a storm before Raffael put them in front and Max Kruse added a second for Lucien Favre's men before the interval.
Havard Nordtveit was sent off midway through the second half and Milos Jojic reduced the arrears with 13 minutes to go, but Dortmund were unable to find an equaliser as they lost to Gladbach for the second time this season.
Jonas Hofmann had the first shot of the game, but Gladbach missed a better opportunity in the 12th minute when Patrick Herrmann touched the ball forwards with his shoulder before flashing a shot wide of the far post.
Dortmund were otherwise in control of the game and Mats Hummels powered his way through in the 21st minute, winning a couple of rebounds before shooting straight at Marc-Andre ter Stegen.
From the resulting corner, Nuri Sahin's volleyed shot was deflected behind for another corner as Dortmund started to build up a head of steam.
Pierre-Emerick Aubameyang rattled the crossbar with another effort before seeing a close-range header saved, albeit with the offside flag already raised.
But just like in the reverse fixture, when Gladbach withstood fierce pressure but still managed to win 2-0, they took the lead in the 31st minute when Herrmann's cross was touched in from close range by Raffael, who appeared to be trying to control the ball as he instead diverted it just inside Roman Weidenfeller's post.
Ten minutes later, Kruse received the ball inside the area, turned inside and then back out to his left, wrong-footing both Weidenfeller and Lukasz Piszczek before slotting the ball in.
For the second time this season, Dortmund found themselves two goals down to the Foals despite dominating the game.
Nordtveit did them a favour when he picked up a second yellow card in the 69th minute, and Dortmund turned up the heat even further.
They pulled one back when Jojic's volley from the edge of the area took a deflection on its way in and they thought they had found an equaliser when substitute Marvin Duksch scored, but the goal was ruled out for a foul by Robert Lewandowski on Ter Stegen.