Thomas Tuchel's men slipped to defeat thanks to goals from Admir Mehmedi and Javier Hernandez are now lie four points behind the German champions after six games
Borussia Dortmund missed the chance to move within a point of Bayern Munich in the Bundesliga table as they were beaten 2-0 by Bayer Leverkusen at the BayArena.
Carlo Ancelotti's men dropped two points against Koln earlier on Saturday, but Dortmund failed to take advantage and lost further ground on the defending champons.
Admir Mehmedi handed Leverkusen an early lead when he headed home a corner from Hakan Calhanoglu.