Match ends, 1. FC Köln 0, FC Bayern München 1.
Robert Lewandowski's 25th Bundesliga goal of the season kept Bayern Munich on course for a fourth successive domestic title as they won at Cologne.
The striker beat keeper Timo Horn with an angled shot after Dominique Heintz half-cleared a Thiago Alcantara cross.
Anthony Modeste and Leonardo Bittencourt came close to an equaliser late in the second half.
But Pep Guardiola's side held on and sit eight points clear of Borussia Dortmund, who visit Augsburg on Sunday.
Guardiola rested Philipp Lahm, Thomas Muller, Frank Ribery and Arturo Vidal following Wednesday's 4-2 Champions League round of 16 second-leg extra-time victory over Juventus.
With Mario Gotze also on the bench, it meant that Bayern had three World Cup winners, a Copa America winner and a Ballon d'Or runner-up to turn to if things turned sour.
There seemed little danger of that as the German champions opened the scoring after nine minutes with their first shot on target.
Poland international Lewandowski's finish was his 42nd in all competitions for club and country this season - while his Bundesliga total of 25 is his highest league tally in one campaign.
With Bayern happy to hold on to their lead, Cologne started to create chances in the second half, and could even have snatched a draw had striker Modeste shown more poise in front of goal.
The Frenchman's best chance came on 73 minutes, but David Alaba was able to block his follow-up effort after Bayern goalkeeper Manuel Neuer had only half saved his initial shot from Marcel Risse's inch-perfect pass.
Bittencourt then almost netted with the final kick off the match, but Neuer made a sprawling stop to secure a 17th clean sheet from 27 league matches.
- 4SörensenBooked at 89mins
- 33LehmannSubstituted forMladenovicat 85'minutes
- 31GerhardtSubstituted forOsakoat 62'minutes
- 13Ferreira de Souza
- 14AlonsoSubstituted forVidalat 54'minutes
- 20RodeSubstituted forLahmat 78'minutesBooked at 86mins
- 6Thiago Alcántara
- 11Douglas CostaSubstituted forRibéryat 72'minutes
- Tobias Welz
- Shots on Target
Second Half ends, 1. FC Köln 0, FC Bayern München 1.
Attempt saved. Leonardo Bittencourt (1. FC Köln) right footed shot from the right side of the six yard box is saved in the centre of the goal. Assisted by Marcel Risse.
Hand ball by Franck Ribéry (FC Bayern München).
Attempt missed. Kingsley Coman (FC Bayern München) left footed shot from the left side of the box is high and wide to the left. Assisted by Robert Lewandowski.
Arturo Vidal (FC Bayern München) wins a free kick in the defensive half.
Foul by Dominic Maroh (1. FC Köln).
Frederik Sörensen (1. FC Köln) is shown the yellow card for a bad foul.
Franck Ribéry (FC Bayern München) wins a free kick in the defensive half.
Foul by Frederik Sörensen (1. FC Köln).
Corner, FC Bayern München. Conceded by Jonas Hector.
Corner, FC Bayern München. Conceded by Timo Horn.
Attempt saved. Robert Lewandowski (FC Bayern München) right footed shot from outside the box is saved in the bottom left corner. Assisted by Thiago Alcántara.
Philipp Lahm (FC Bayern München) is shown the yellow card for a bad foul.
Foul by Philipp Lahm (FC Bayern München).
Leonardo Bittencourt (1. FC Köln) wins a free kick in the attacking half.
Substitution, 1. FC Köln. Filip Mladenovic replaces Matthias Lehmann.
Offside, 1. FC Köln. Leonardo Bittencourt tries a through ball, but Yuya Osako is caught offside.
Kingsley Coman (FC Bayern München) wins a free kick on the right wing.
Foul by Dominique Heintz (1. FC Köln).