Franck Ribery was sent off in the first half but Bundesliga top-scorer Mario Gomez notched his 16th league goal of the season to put the hosts in front after 48 minutes.
Substitute David Alaba made it 2-0 from close range and Toni Kroos grabbed the third goal two minutes from time with a delicate chip from 10 metres.
"Cologne were mixing concrete at the back today and played extremely defensively," Bayern coach Jupp Heynckes told reporters.
"After Franck's dismissal it was even harder for us but the team reacted very well, kept a tight defence and went forward to score the goals. We dominated the game even with 10, that was class."
The France forward went down in the penalty box and lost his temper with Sereno, pushing his opponent's head after the Portuguese told him to get up.
