The Billy Goats were well and truly beaten at home, which, coupled with Hertha's win over Hoffenheim, confirmed their descent into the 2.Bundesliga next season
Thomas Muller struck in either half alongside an effort from Arjen Robben and an own goal by Pedro Geromel, meaning that a lone consolation from Milivoje Novakovic was nowhere near enough.
Hertha Berlin's 3-1 win over Hoffenheim propelled them into the relegation play-off ahead of Koln by a point, who saw the closing stages of the match disrupted by a few unruly fans as their relegation to the 2.Bundesliga became inevitable.
Bayern, already assured of second place, began to grow into the game after a slow start. Mario Gomez fired a warning shot to Koln after 20 minutes, firing inches wide after showing good footwork to create space.
The home side were back at the other end of the pitch within minutes, and a powerful blast from Lukas Podolski forced Manuel Neuer to save spectacularly.
However, despite encouraging play by the hosts, it was Bayern who found themselves just after the half-hour mark. Franck Ribery’s ball across the face of goal was not dealt with by the Koln defence, and Muller was afforded the freedom of the RheinEnergieStadion to volley home.
Ribery almost doubled the visitors’ advantage within moments of the restart, but fizzed a shot wide after finding an opening on goal.
Heading into the break, Koln knew that they needed to find a goal, given that Hertha were also ahead against Hoffenheim at half-time.
However, the wind was taken out of their sails seven minutes into the second period, as a low cross by Ribery was inadvertently turned into their own net by defender Geromel.
The hosts were then completely floored by the third Bayern goal within moments of the restart. Toni Kroos picked out Robben in space, and the Dutchman made no mistake, firing his finish high into the net.
Gomez nearly added another on the hour mark after rounding Michael Rensing, but he could not find the target as the angle diminished in front of him.
The home side did manage to pull one back though, Novakovic finishing cooly ahead of Anatoliy Tymoshckuk after being found by the impressive Podolski.
However, the game was well out of Koln’s reach at this point, turning the remainder of the encounter for the home side into a game of wait and hope.
Their prayers were not answered, however, as news filtered through of Anis Ben-Hatira’s second goal for Hertha against Hoffenheim, putting Koln on the brink of relegation.
None of the fans showed any signs of leaving early though, even after Muller’s cheeky backheel with five minutes to go that put the score at 4-1.
Word of Hertha’s 3-1 victory spread around the stadium was too much for a few supporters, who set off flares that covered the ground in a thick blanket of smoke.
The players were ushered from the field straight from the final whistle, and hordes of police stepped out onto the pitch as Koln’s Bundesliga campaign ended in chaos.