A Robert Lewandowski goal ended the resistance of rock bottom Cologne as Bayern Munich extended their Bundesliga lead to nine points with a 1-0 win.
With Bayern having dropped points in only four games this season and Cologne managing just three points and no victories from their first 15 games, this was a total mismatch on paper.
But Cologne head coach Stefan Ruthenbeck had vowed his players would not "stand in front of a big beast like a little mouse," and they took away a lot of respect, if no points, from the Allianz Arena.
Bayern had 84 percent of possession in the first half and 12 shots but Timo Horn was not called upon to make too many saves.
But Cologne's valiant efforts were undone by a fine move on the hour mark finished off by Lewandowski for his 21st goal of the season.
The goal maintained his record of having scored in every home game in the Bundesliga this season.
Still, the visitors nearly secured a point, with Lukas Klunter denied by a fine save by 36-year-old Tom Starke three minutes from time.
Cologne knew they were in for a long evening and efforts were soon raining in on their goal.
From an 11th-minute corner, Lewandowski smashed in a shot that took a deflection and sailed over the bar.
Two minutes later Franck Ribery played a sublime ball over the top to Thomas Muller but his first touch was just too heavy and Horn was able to save the resulting shot.
Niklas Sule was the next to try his luck with a header over the bar, and from there the golden chances rather dried up.
In fact, the best opening during the rest of the half came on the break for Cologne but Milos Jojic's chip was deflected over the crossbar.
Bayern coach Jupp Heynckes took action at half-time, sending on Kingsley Coman and James Rodriguez in place of Arturo Vidal and Corentin Tolisso.
The hosts really should have taken the lead six minutes after the break but, from Muller's superb cross, Lewandowski uncharacteristically sent a close-range header over the bar.
Bayern's frustration was growing but with an hour gone they put together an incisive move that Cologne were powerless to resist.
Jerome Boateng floated in a pinpoint ball that Muller header into the path of Lewandowski, who this time made no mistake.
The goal seemed to give Bayern an extra gear and, after Horn had saved well from James, Coman headed a Boateng cross into the turf and against the bar.
Sule then sent in a stinging shot that Horn repelled with his fists before the keeper produced probably his save of the night from James' curling effort.
Cologne had offered very little in attack in the second half but they very nearly snatched a point, Starke sticking out a hand to prevent Klunter netting the unlikeliest of equalisers.