Koln extended their winless run to six matches following a 1-1 draw at Augsburg on Sunday night.
After a Florian Niederlechner missed a 27th minute penalty for the home side, Anthony Modeste put the visitors ahead in the 85th minute.
Philipp Max got the equaliser three minutes later to secure a point for the home side.
Werder Bremen's relegation woes continued after a 1-0 home defeat to Wolfsburg on Sunday.
Wout Weghorst's 12th goal of the season in the 82nd minute secured the spoils for the visitors, who move up to sixth spot.
Bremen, meanwhile, remain missed the chance to move level on points with 16th-placed Fortuna Dusseldorf.
Schalke and Union Berlin had to settle for a share of the spoils after playing to a 1-1 draw on Sunday afternoon.
Robert Andrich had Berlin ahead as early as the 11th minute but Jonjoe Kenny's 28th minute equaliser secured the point for David Wagner's side.