Unable to beat Leverkusen in six attempts since Xabi Alonso took over in October 2022, Bayern were dominant from start to finish against the German champions, who looked shellshocked under the Allianz Arena floodlights.
Kane headed in a lovely Michael Olise cross after nine minutes. Nine minutes into the second, Jamal Musiala was in the perfect spot to capitalise on a goalkeeping howler from Matej Kovar, the usual backup to Leverkusen captain Lukas Hradecky.
Kovar rose high but not high enough, allowing a tame Joshua Kimmich chip to slip through his fingers. The ball fell at the feet of a grateful Musiala, who tapped home. Eight minutes later, centre-back Nordi Mukiele sunk his studs into the calf of Alphonso Davies, picking up a second yellow.
Mukiele's replacement Edmund Tapsoba bear hugged Kane in the box. After the England captain fell to the turf, referee Michael Oliver consulted the VAR screen and pointed to the spot.
Kane converted as he has in every match dating back to his miss for England against France in the 2022 World Cup, putting Bayern on course for a victory in the tie and keeping the dream alive of appearing in this season's final in Munich.