Dortmund maintained the nucleus of the line-up that edged Arminia Bielefeld in the Bundesliga on Saturday, while Alassane Plea as ever lead the front for the home side.
A substitution as soon as the fifth minute threw Dortmund's game-plan in disarray, as Nico Schulz had to enter from the bench to replace Raphael Guerreiro through an injury.
Gladbach aimed to take the situation in their stride moments thereafter as a close-range opportunity found Marcus Thuram, who unfortunately failed to capitalise.
Following a rather quiet opening quarter, Dortmund carved their first opening after the half-hour mark through Erling Braut Haaland but he directed wide of the mark.
Both sides emerged for the second half keen to stamp their ground on the overall clash with no substitutions at the break taking place.
Dortmund went into the lead on 53 minutes through a clever strike from Haaland, but the Video Assistant Review (VAR) reviewed and chalked off the finish following a foul in the build-up.
The Black and Yellow were put to a bit of defending 60 minutes in after Ramy Bensebaini brought goalkeeper Marwin Hitz to a stupendous save with an equally stupendous attempt.
However, the fears were allayed by the visiting side six minutes later as Jadon Sancho propped up on the far side to guide home a delivery from Marco Reus following a swift counter-attack.
Dortmund searched for a second late on and nearly found it through Haaland, but he was denied by Gladbach goalkeeper Tobi Sippel.
The Black and Yellow ended the match with ten players in stoppage time after Mahmoud Dahoud saw red for a second bookable offence, however it didn't matter as it finished 1-0.