The 33-year-old England striker achieved the milestone by converting a 39th-minute penalty on Friday (Saturday AEST) to extend Bayern's lead to 3–0 before halftime.
Jamal Musiala had opened the scoring in the 18th minute and Michael Olise added another in the 43rd.
Kane struck again in the 54th, bringing his total to 101 goals in 99 matches. The previous record for the fastest to a century was set at 123 games by Dieter Müller, a prolific striker for Cologne in the 1970s.
Olise then completed a hat-trick in the 73rd and 76th. Ismael Saibari was also on target.
Following two unconvincing Bundesliga performances against promoted teams, a goalless draw with Schalke and a 2-1 win over Elversberg, the victory gave Bayern 10 points through four matches.
In France, Monaco continued their impressive start to the season under new coach Filipe Luis, defeating Lens 2-1 to remain unbeaten at the top of Ligue 1.
Paris Brunner put Monaco ahead in the 32nd, but Matthieu Udol equalised in the 57th. Jonathan Gradit then scored an own goal in the 84th.
Brunner is still awaiting a likely sanction for a throat-slitting gesture during a goal celebration last weekend.
Lens coach Dino Toppmöller was dismissed in the week after just six games in charge.
In Italy, Gustavo Varela scored twice as Monza pulled off an upset by beating Sassuolo 2-1 to secure their first Serie A win of the season.
Varela found the net in the 51st and 63rd for the Biancorossi, who had lost three of their opening four matches.
Vasilije Adžić pulled a goal back for Sassuolo in the 88th, but it was a disappointing night for a side coming off a 3–2 victory over Juventus.
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