The hosts may have come into this as heavy underdogs, but they showed intent right from the start, with Said El Mala forcing a save from Manuel Neuer inside 90 seconds.
There was a significant delay shortly after due to the smoke coming from flares in the stands, but while the smoke eventually faded, Koln were determined not to give in, with Linton Maina delivering a cross that was awkwardly dealt with.
Even so, Bayern had efforts of their own as Marvin Schwabe denied Hiroki Ito and Michael Olise before tipping a venomous Serge Gnabry strike past the post.
A bizarre moment followed as Schwäbe completely missed Jahmai Simpson-Pusey’s backpass before the ball trickled marginally wide.
Maina fully capitalised on his goalkeeper’s reprieve to leave the visitors stunned in the 41st minute, as he won the ball near Koln’s box and raced right up the pitch before hitting a shot that beat Neuer despite the goalkeeper getting both hands to it.
Die Geissbocke’s lead only lasted until the fifth minute of first-half stoppage time, though, as Gnabry conjured an ingenious touch and finish that bounced over Schwäbe on its way into the net.
Bayern initially had a greater level of control after the restart, but that didn’t translate to a goal, with Olise’s free-kick and an improvised Gnabry slip being routinely saved. While Jakub Kaminski was overpowered by Kim Min-Jae when he tried to run behind, the Poland international tested Neuer shortly after.
Luis Diaz and Leon Goretzka then both fired harmlessly off-target before an Ito attempt was deflected behind. Bayern went ahead following successive corners, as the ball was worked to Díaz and his ball in was nodded down by Ito for Kim to convert.
Díaz then danced through the box and laid the ball off for Lennart Karl to apply the coolest of finishes to wrap up the win for Bayern.
That saw the Bavarians beat their own record for the best-ever first half to a Bundesliga season, with their tally of 47 points also putting them 11 points ahead of second-placed Borussia Dortmund.
Koln can certainly take encouragement from their performance, although Die Geissbocke have now lost three of their last four Bundesliga matches.
Flashscore Man of the Match: Serge Gnabry (Bayern Munich)