Kane beat goalkeeper Frederik Ronnow to score Bayern's second goal of the evening from the penalty spot after 39 minutes.
He added a second in the 54th minute.
Cologne's Dieter Muller held the previous record for reaching 100 Bundesliga goals after 129 matches in the early 1970s.
Across Europe's five major leagues only Cristiano Ronaldo took less time to reach this symbolic milestone, doing so in 92 matches with Real Madrid in La Liga in the early 2010s.
After joining Bayern in the summer of 2023, Kane finished the top scorer in each of his three Bundesliga seasons with 36 goals in 2023–24, 26 goals in 2024–25 and 36 goals in 2025–26, winning the European Golden Boot twice in the summers of 2024 and 2026.
This season, he opened his Bundesliga scoring account last week in Elversberg, netting the winning goal in Bayern's 2-1 victory.