- He also became the first Englishman to score 18 times in a Bundesliga season.
- The victory takes Bayern one point ahead of Bayer Leverkusen, who play their game in hand on Saturday.
England captain Harry Kane scored again as Bayern Munich won at Cologne to move top of the German Bundesliga table.
Kane's goal was his 18th in 12 league matches and he also became the first Englishman to score 18 times in a Bundesliga season.
He finished from close range in the 20th minute after Eric Maxim Choupo-Moting's shot was cleared off the line.
The victory takes Bayern one point ahead of Bayer Leverkusen, who play their game in hand on Saturday.
Leverkusen, the only other unbeaten side in the German top flight, will regain top spot if they win at Werder Bremen.
Bayern's match was their first against Cologne since beating them 2-1 in May when Jamal Musiala scored a last-minute winning goal to beat Borussia Dortmund to the title. Dortmund would have become champions for the first time since 2011-12 if they had defeated Mainz, but instead drew 2-2.
Since then, Bayern have signed Kane from Tottenham in an £86.4m deal as they bid for a 12th consecutive Bundesliga title.
Against Cologne, Kane was at the heart of Bayern's best moves and they almost went ahead when his pass found Leroy Sane, but the former Manchester City forward could not lift the ball over home goalkeeper Marvin Schwabe.
But Bayern did not have to wait long before going ahead.
Sane played it to Choupo-Moting, he cut inside and had a shot cleared off the line by Julian Chabot, with Kane tapping home the rebound.
As well as becoming the top-scoring Englishman in one Bundesliga season, the 30-year-old became the first player in league history to have scored 18 times after the opening 12 matchdays.
England's record goalscorer has 22 goals in 17 appearances in all competitions for Thomas Tuchel's side.
Choupo-Moting, Sane and Kingsley Coman missed chances to double Bayern's advantage.
Davie Selke had a rare chance for Cologne, who drop to the bottom of the table, but failed to beat Manuel Neuer with a header at the back post.
Coman hit the crossbar in the second half, and the hosts then offered little as an attacking threat as Bayern took the victory.