Cologne’s relegation fears deepened after a 3-1 defeat at Werder Bremen.
The hosts took the lead in the 33rd minute when Milos Veljkovic arrived unmarked at the far post to sweep home Zlatko Junuzovic’s corner.
Yuya Osako equalised for Cologne eight minutes after the interval when he drove into the top corner.
But they were level for just five minutes before Florian Kainz played in Milot Rashica to slot home.
Claudio Pizarro almost added a third but his header flew narrowly wide and Thomas Delaney was also off target with a fierce drive.
Cologne were finally killed off in the last minute when Maximilian Eggestein raced on to Zlatko Junuzovic’s through-ball and tucked it away.
The defeat left Cologne rooted to the foot of the table, eight points adrift of safety.