Bayern Munich dominated the match with two goals from Harry Kane and two assists from Thomas Müller, while Cologne struggled to find their rhythm in the final third.
Kane opened the scoring for Bayern Munich just before half-time, taking advantage of a poor clearance by Cologne's goalkeeper to fire past him. The England forward then doubled his tally in the second half when he scored from close range after being played through by Müller.
Müller also contributed two assists, one coming in the first half when he fed Kane on the edge of the box, and another in the second half when he played the ball into the path of Thomas Müller, who scored from distance.
Cologne tried to get back into the game in the second half but could not create enough chances. They had several opportunities to score, including a header from the corner that was cleared off the line, but they failed to capitalize on them.
The result means Bayern Munich continue their unbeaten run in Bundesliga this season, which now stands at 12 games without losing. They move up to second place in the table, only one point behind leaders Borussia Dortmund.
For Cologne, the loss is particularly disappointing given their recent form. They have won three of their last four matches, but were unable to capitalize on their opportunities against Bayern Munich.
Overall, it was a dominant performance from Bayern Munich, who showed why they are considered one of the best teams in Europe. They will hope to build on this win and continue their impressive run in the Bundesliga.