Cologne secured their top-flight status for next season and jeopardised Schalke's hopes of qualifying for Europe next season with a narrow but deserved 2-0 win on Sunday.
Marcel Risse opened the scoring for the Goats, who wasted several opportunities to win more convincingly against a Schalke side who were simply not at the races, adding a second only in the final minute through Yannick Gerhardt.
The Royal Blues must ensure they bounce back in their final two games with just a two-point advantage over seventh-placed Borussia Dortmund and Werder Bremen in eighth as they risk not making it into Europe at all next season.
On Sunday's evidence, Schalke would find it hard to justify being one of the Bundesliga's representatives in Europe after being played off the park by Cologne.
Only the hosts showed any hunger, although they were too wasteful in front of goal before Risse gave them the lead in the 34th minute.
He crowned an excellent team move involving a succession of first-time passes which sliced through the Schalke defence before Kazuki Nagasawa's shot was parried by Ralf Fahrmann to Risse, who threaded the rebound into the unguarded goal.
Another quick move saw Svento put through with only Fahrmann to beat, but as easy as it was to get him into a shooting position, he made the finish look hard by curling his effort wide of the far post.
It was a let-off for Schalke, but they showed no clear intention to do anything about it.
Kevin-Prince Boateng - their hero a week ago - was anonymous in an attack which was lacking the suspended Klaas-Jan Huntelaar and injured Jefferson Farfan, whose season is over.
Risse wasted another late chance to put the game to bed, but Cologne's wastefulness was not punished as Schalke appeared too tame to make any impression. Gerhardt then settled any nerves with a second in the last minute as Schalke succumbed to a defeat which leaves them still with plenty of work to do to make it into Europe next season.
ends
German Bundesliga Standings
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