With his first goal at the Allianz Arena, Kane expertly found the back of the net from the penalty spot as is customary.
And his second was the kind of thing Bayern fans haven't seen since Robert Lewandowski departed the club, with Kane netting the perfect poacher's goal.
Seeing Alphonso Davies making space for a cross down the left hand side, the former Tottenham striker spotted a space and got on the end of his pass for a simple dink into the back of the net.
Lighting up the Arena in Munich, Kane got a high-five from a fan as his beaming smile looked perfectly in place at his new home.
His strikes came after an own-goal from Felix Uduokhai, with Dion Drena Beljo finding a late consolation.
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The result leaves Bayern in second spot in the Bundesliga with a maximum six points. Union Berlin are top having scored more goals than the reigning champions.
Kane netted on his Bayern debut last weekend, which saw them win 2-0 at Werder Bremen. The England captain got an assist for Bayern's other goal.