The home side pressured early and took the lead in the 37th minute when Geromel nodded home past goalkeeper Alexander Stephan after a wonderful cross by Adli Chihi.
Milivoje Novakovic doubled the advantage for Köln in the 70th minute as he put a shot past Stephan following Lukas Podolski's cross. The Slovenia international striker doubled his tally just seven minutes later when he headed home a cross by midfielder Petit.
Nürnberg's misery was complete six minutes from time when Juri Judt was dismissed for a second yellow card.
Köln are up to 12th place ahead of the German winter break while Nürnberg sit comfortably in the relegation zone, second from bottom on just 12 points.