Ten-man Bayern Munich opened a six-point advantage at the top of the Bundesliga on Friday, a 3-0 win over Cologne ensuring they will go into the winter break as leaders.
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.
Bayern have 37 points from 17 games. Second-placed Borussia Dortmund, the champions, are on 31 and visit bottom club Freiburg on Saturday.
"Cologne were mixing concrete at the back today and played extremely defensively," Bayern coach Jupp Heynckes said.
"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."
Ribery, who was ordered to pay his former agent 2.66 million euros in unpaid commission earlier on Friday, was sent off in the 33rd minute after receiving two quickfire bookings.
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.
Sereno continued to talk to Ribery who then grabbed him by the throat and was given a second yellow card.
Bayern, who failed to win their previous five home games against Cologne, went in front when Gomez tapped the ball in following a defensive error by visiting captain Pedro Geromel.
With Cologne failing to make the extra man count, Austria international Alaba fired in at the far post after a corner sailed past the entire defence.
Kroos made sure of the win by lifting the ball over keeper Michael Rensing.
The winter break starts on Monday and ends on January 20.
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