The margin of victory may have looked comprehensive, and they could have scored at least double that, but had it not been for some excellent saves from Manuel Neuer, Bayern would have conceded at least four also.
Bastian Schweinsteiger gave the hosts an early lead and Franck Ribery added a second, but the floodgates refused to open.
Anthony Ujah pulled one back on the stroke of half-time and Cologne enjoyed a good spell of pressure early in the second half before Arjen Robben and Robert Lewandowski sealed Bayern’s fourth Bundesliga win in a row.
When Schweinsteiger headed Robben’s corner past Horn in the third minute, thoughts were already turning to how many Bayern were going to put past Cologne.
Lewandowski nearly added a second in the 10th minute only for Timo Horn to make a save, but the ball came back within 10 seconds with Ribery dribbling it inside and placing his shot to the left of an immobile Horn.
It was already looking easy for Bayern, but the goal fest did not materialise and, right on the stroke of half-time, Ujah made things interesting with a header from six yards out.
Cologne came out fighting and had Bayern up against the ropes when Neuer made a fine save to turn Ujah’s header wide.
From the corner, Marcel Risse brought another excellent save out of Germany’s number one and suddenly, it was Cologne laying siege to the Bayern goal.
The complex of the game could and perhaps should have changed when Robben was sent clear, but his attempt to tee up Lewandowski was cut out at full stretch by Miso Brecko.
Robben restored Bayern’s two-goal lead with an unstoppable header from Ribery’s cross, but had Neuer not made yet another world class save to deny Daniel Halfar, Cologne could have been right back in it for the final 15 minutes.
It took Lewandowski to settle any lingering nerves, turning Robben’s pass in with his chest before Horn ensured it did not get worse with a save matching any of Neuer’s to deny Robben a fifth.