Kane headed in for his fourth goal in four Bundesliga games before Alex Grimaldo levelled with a brilliant free-kick into the top corner.
Leon Goretzka scored what looked like a Bayern winner with four minutes to go from Mathys Tel’s cutback.
But Exequiel Palacios netted a penalty, awarded by the video assistant referee, in injury time to rescue Leverkusen.
Dayot Upamecano thought he had scored Bayern’s winner with almost the last kick but it was ruled out for offside.
Kane’s close-range opener made him the first Bayern player to score four goals in his first four Bundesliga games since Miroslav Klose in 2007.
It brought his club career total to 300, with 280 for Tottenham, nine for Millwall, five for Leyton Orient, four for Bayern and two for Leicester.
Bayern and Leverkusen both lose their 100% starts to the season but maintain their unbeaten records.
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