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.