Kane drilled into the bottom corner from long range in the 57th, struck again three minutes later, and tapped home the third in the 80th in Saturday's clash.
Kingsley Coman wrapped up matters against last season's runners-up in the 89th as Bayern ended a run of three games without victory, getting confidence for next week's Champions League trip to Barcelona where they will face their former coach Hansi Flick.
Kane scoring one of his treble in the 4-0 win over Stuttgart. (AP PHOTO)
Bayern retained first place in the table for another matchday, ahead on goal difference over RB Leipzig who won 2-0 at Mainz, with goals from Xavi Simons and Willi Orban. Freiburg are third after beating Augsburg 3-1.
Champions Bayer Leverkusen also returned to winning ways when Victor Boniface and Robert Andrich made up for earlier blunders in a 2-1 comeback victory over in-form Eintracht Frankfurt, who had led through league top scorer Omar Marmoush.
It was Leverkusen's first win after two league draws and rocketed them back into fourth past Frankfurt, whose unbeaten run ended after five games.
For Kane, it was a day to celebrate his seventh hat-trick in a Bayern shirt.
"We didn't find a way in the previous games and in the first half. We took the game to another level in the second half," Kane told Sky TV.
Of his first goal, he added: "It was nice to see it go in and from then on the game opened up. I believe in myself and my ability and my teammates."
Elsewhere, new Germany striker Tim Kleindienst scored a brace for Borussia Monchengladbach in a 3-2 victory against his former club Heidenheim.
Hoffenheim ended a run of five games without victory by beating winless bottom club Bochum 3-1.
On Friday, Borussia Dortmund had defeated Jackson Irvine's St Pauli 2-1.
