The hosts came into the match two points ahead of their local rivals but it was the visitors who had the first opportunity of the game when the ball broke to top scorer Anthony Modeste in the box, but the striker's effort was blocked by Bernd Leno.
Leverkusen top-scorer Javier Hernandez tested Timo Horn with a curler from the edge of the box as his side began to find a foot in the match, but it was the visitors who broke their month-long goal drought to take the lead minutes later.
Marcel Risse's free kick was flicked on to the feet of Maroh and the defender turned the ball home first time to break the deadlock.
Horn kept the away side in the lead with saves from Karim Bellarabi and Kevin Kampl as Leverkusen pressed for an equaliser immediately, and the leveller arrived just after half an hour when Hernandez capitalised on poor defending to head home his 10th of the season.
Modeste backheeled wide for Koln shortly after the restart as both sides sought the crucial third goal of the game, and the visitors were handed a boost shortly afterwards when Kyriakos Papadopoulos was shown a straight red card for bringing the striker down as he tried to run through on goal.
Koln made their numerical advantage pay with 18 minutes remaining through the same combination as for the opener, with Maroh meeting Risse's corner with a bullet header to secure a first win in five games and condemn their rivals to defeat.