Needing to win the game to secure a place in a play-off to avoid relegation, Frank Schafer's side were unable to get the better of their own nerves and succumbed to two goals from Thomas Muller, a Pedro Geromel own goal and an Arjen Robben strike.
Milivoje Novakovic scored a consolation for the home side, who had to run for the safety of the dressing rooms with Bayern's players at the final whistle as the home fans' anger overspilled.
It was a day of destiny in Cologne, and that destiny was within their own hands as a win would have saved them from automatic relegation, no matter what happened between Hertha Berlin and Hoffenheim in the capital.
However, the home side appeared nervous as they welcomed the record German champions, who fielded a strong team a week before the DFB-Pokal final against Borussia Dortmund.
Bayern confirmed that they were taking this game seriously as they were immediately on the attack with Mario Gomez searching for the top goalscorer crown.
Michael Rensing prevented him from getting a header in on goal i the 14th minute when he punched Franck Ribery's cross away.
Ribery was the provider of the opening goal in the 34th minute when he sent in a cross from the right to the unmarked Muller, who had time to control the ball and pick his spot past his former team mate Rensing
It was a goal which, with Berlin leading against Hoffenheim, meant Cologne were on course for relegation, and the first 10 minutes of the second half further condemned them.
Geromel scored an own goal which was typical of Cologne's woes and summed up why they would be playing in the second division next season.
His attempted clearance from Ribery's cross hit Kevin McKenna and ricocheted back off his own leg into the goal.
Two minutes later, Robben made it three for Bayern when he powered in a shot into the roof of the net from Toni Kroos's cross with the Cologne defence once again all at sea.
Novakovic gave the home team a glimmer of hope when he pulled a goal back in the 63rd minute, turning Lukas Podolski's cross past Manuel Neuer.
But the joy was short-lived as the news filtered through that Hertha had gone two up against Hoffenheim, effectively sealing Cologne's fate as they followed Kaiserslautern down into the second division.
Muller added a fourth for Bayern and that goal proved to be too much for some Cologne fans, who lit thick black smoke bombs and spilled onto the pitch.
The referee decided to blow the final whistle a few seconds early with both sides running for refuge as Cologne striker Lukas Podolski remained almost alone on the field at the end of his final game for the club, leaving with a lasting but not particularly pleasant memory.