Die Schwarzgelben entered this contest following consecutive defeats that knocked them out of the UEFA Champions League and significantly damaged their Bundesliga title hopes.
They narrowly avoided another setback within five minutes at the RheinEnergieStadion, as Ramy Bensebaini blocked two Isak Johannesson shots in quick succession and Gregor Kobel tipped Youssoupha Niang’s header over the crossbar.
However, Johannesson’s lax pass offered the visitors the opportunity to spring forward, and while Tom Krauss deflected Maximilian Beier’s timid attempt behind, the hosts couldn’t convincingly clear the ensuing corner, and Serhou Guirassy instinctively poked the ball home.
Niang and Saïd El Mala could only fire into side-netting as the away team looked for an immediate response, while Dortmund appeared to be buoyed by the opener, with Beier seeing a shot blocked by Rav van den Berg between those Koln attempts.
An awkward Kristoffer Lund header at the other end went unpunished as Marvin Schwabe denied Guirassy, but Koln suffered another blow before the break when an initial yellow card shown to Jahmai Simspon-Pusey for a challenge from behind on Beier was upgraded to a red following a VAR check.
Lukas Kwasniok shored up his defence by bringing on Cenk Ozkacar for Johannesson ahead of the restart, but the hosts still showed moments of intent, with Jakub Kaminski’s shot being parried by Kobel before Daniel Svensson had to scramble to stop Niang from scoring the rebound.
Even so, Dortmund had looked positive and added a second on the hour mark, when Beier played a one-two with Julian Brandt and effortlessly stroked the ball past Schwabe.
The visitors looked imperious after doubling their lead, although Felix Nmecha and Bensebaini both struck wide from promising positions.
Those misses and a deflection off Waldemar Anton helping Kaminski’s attempt beat Kobel caused late nerves for Dortmund, but the visitors still picked up their first win from their last four matches across all competitions. The result at least keeps the gap from Bayern Munich at 11 points, while Die Schwarzgelben sit six points ahead of third-placed TSG Hoffenheim.
Meanwhile, a fourth loss in five for Koln leaves them two points above the relegation play-off place before St Pauli and Werder Bremen play on Sunday.
Flashscore Man of the Match: Maximilian Beier (Borussia Dortmund)