Leverkusen were keen to respond after suffering back-to-back defeats in the Bundesliga, and they were certainly the team in the ascendancy in the first half.
Defender Edmond Tapsoga had the first opportunity for the home side with seven minutes on the clock when his effort from outside the area went just wide of the right post. Christian Michel Kofane was next to come close for the hosts, but his effort from inside the box was saved by Marvin Schwabe.
Despite the control Die Werkself had in the first half, it was the visitors who created arguably the best opportunity before the break when Said El Mala broke into the area and squared the ball to Luca Waldschmidt, but the forward was unable to sort his feet out in time, and the chance went begging.
Mark Flekken was equal to Waldschmidt’s effort just after the half-hour mark, before Robert Andrich spurned a presentable opportunity when he headed wide of the right post from close range despite being unmarked.
Both teams knew that the first goal would be vital, and it was Leverkusen who had the first big chance after the restart when Malik Tillman broke through and sent his effort from the edge of the area over the crossbar.
With Koln hanging on but still very much in the contest, the visitors could have taken the lead when Sebastian Sebulonsen’s free-kick from 25 yards was heading for the bottom right-hand corner, but Flekken was equal to his effort.
The home supporters would have been forgiven for thinking that it wasn’t going to be their day.
However, with just under 25 minutes remaining, they took the lead in stunning fashion when Arthur’s cross picked out Terrier, who produced a scorpion kick effort which looped over Schwabe and into the net.
With much of the pressure eased, Andrich made sure of the victory by netting six minutes later to claim a result which lifts Leverkusen into the top four.
Cologne remain in the very respectable position of ninth, although there is only a five-point gap to the relegation zone.
Flashscore Man of the Match: Martin Terrier (Bayer Leverkusen)