The former Tottenham striker scored the opening goal with a low shot from just outside the penalty area in the 13th minute and nears what would be the first major team trophy of a career filled with individual scoring accolades.
The England captain is the fastest player to 60 goals in Bundesliga history, beating Erling Haaland's mark of 65 games with Borussia Dortmund.
Bayern moved nine points clear of second-placed Bayer Leverkusen, who play St. Pauli on Sunday, with four games remaining after this week.
Konrad Laimer scored Bayern's second goal on the counter six minutes after Kane's opener and Kane played a part in the build-up.
Kingsley Coman made it 3-0 in the 36th on the rebound after Raphael Guerreiro's shot was saved. Joshua Kimmich added the fourth in the second half.
Union Berlin and Stuttgart set a Bundesliga record with eight goals each before halftime.
Andre Ilic scored twice for 11th-placed Union, while 13th-placed Stuttgart had four different scorers.
Meanwhile, a painful-looking collision left Leipzig goalkeeper Peter Gulacsi and Holstein Kiel defender David Zec needing treatment for concussions and overshadowed their 1-1 draw.
The two players crashed into each other in the 62nd minute while running towards the ball and were briefly knocked unconscious, according to coaches Zsolt Löw of Leipzig and Marcel Rapp of Kiel.
While Zec could leave the pitch dizzy but on his own after a while, Gulacsi was taken off on a stretcher and to hospital for further examinations.
"Peter Gulacsi suffered a concussion and injured his right ear in today's game against Kiel," Leipzig said on X later in the evening.
"He's doing well under the circumstances, but will stay overnight in hospital for observation. Get well soon, Pete," the post said along a photo of Gulacsi in his hospital bed giving a thumbs up sign.
Rapp said at the Kiel news conference after the 1-1 draw: "David is in the dressing room, he is responsive and has concussion. But he is quite OK."
Kiel coach Marcel Rapp said Zec had a concussion and was responsive.
Soon after the incident, Benjamin Sesko's penalty salvaged a draw for Leipzig, which lost ground in the race to qualify for the Champions League.
Leipzig stayed fourth but fifth-placed Freiburg was a point behind following its 3-2 win over Hoffenheim. Mainz was sixth after conceding late in a 2-2 draw with Wolfsburg. Werder Bremen rose two places to seventh by beating Bochum 1-0.
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