The Royal Blues went ahead with goals from Breel Embolo and Yevhen Konoplyanka but Cologne crawled back with Leonardo Bittencourt cutting the deficit in the 26th minute and Marcel Risse securing an unexpected point in the 83rd.
Schalke, who also hit the woodwork, are on 56 points, two ahead of third-placed Borussia Dortmund and seven in front of fifth-placed Hoffenheim, with the top four qualifying for the Champions League group stage.
Despite the point, Cologne still need a miracle to avoid the drop, remaining in last place on 22 points, eight off the relegation playoff spot.
Earlier, Augsburg made sure of another season in the top division with a 2-0 victory over Mainz 05, who are anchored in 15th on 30 points, along with VfL Wolfsburg in 14th and 16th-placed Freiburg.
(Reporting by Karolos Grohmann; Editing by Christian Radnedge)
