Harry Kane became the highest-scoring Englishman in a single Bundesliga season with the only goal of the game as Bayern Munich won 1-0 in Cologne.
Kane finished off the rebound when Eric Maxim Choupo-Moting's effort was cleared off the line after 20 minutes for his 18th goal of the season as Bayern then threatened to blow away their hosts - but were let down by their own poor finishing.
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Choupo-Moting passed up a number of first-half chances while Kingsley Coman hit the bar late on, though Cologne had chances of their own and improved after half-time without seriously threatening Bayern's lead.
While Bayern's win took them top of the table, Steffen Baumgart's side now prop up the Bundesliga after an eighth defeat in 12 games, with their goal difference now inferior to previous bottom side Union Berlin.
How Kane was Abel to make yet more history
Bayern Munich could barely have wished for a more inviting opposition to face to ensure they started the weekend top of the Bundesliga.
And they set the tone in the opening minutes, with Choupo-Moting passing up an early chance before inadvertently teeing up Kane for the opener. Konrad Laimer's bursting run caught the hosts out on the counter, and he saw his goal-bound effort cleared to the England striker for a simple finish.
Leroy Sane nearly made it two within minutes but was denied by Marvin Schwabe, before the same player somehow fired wide from eight yards out with only the goalkeeper to beat.
There was only one moment to concern Thomas Tuchel before the break, when Rasmus Carstensen's back-post header was clawed away by Neuer.
From the restart, Cologne improved but were unable to construct more routes to goal to test Neuer again.
They did at least limit Bayern's impetus after the break and it wasn't until Coman struck the crossbar with a free header from a corner 12 minutes from time that they were finally threatened.
That was the last moment of meaningful action at either end, as Bayern were left to enjoy the result, rather than the performance, which took them top of the Bundesliga for Friday night at least.
Kane: I feel at home here
Harry Kane speaking after the win:
"I'm feeling good. I feel at home here. Everyone's welcomed me really well from the players, the staff, the club, the fans and I just want to repay them every time I step out onto the pitch.
"We've got fantastic players around me who are creating chances for me, so I've just got to make sure I'm in the right place at the right time."
Asked if he is in the best form of his career, Kane replied: "I've had some good moments in my career and good spells, but this is definitely one of the best.
"I feel good going into every game. I know I'm going to get chances going into the game and that was a nice one that fell to my feet there - one of the easier ones I'll probably score in my career."
What's next?
Bayern Munich are guaranteed to finish top of Group A in the Champions League after winning their first four matches. On Wednesday, they host second-place Copenhagen at 8pm.
Bayern return to league action on Saturday December 2 at home to FC Union Berlin, kick-off 2.30pm.