A battling Borussia Dortmund outfit then ended a run of three defeats with a 2-1 comeback victory later on Saturday against RB Leipzig, who suffered their first league loss of the season to fall three points behind leaders Bayern.
Rampant Eintracht Frankfurt proved the day's top marksmen in Germany, thrashing bottom club Bochum 7-2.
For Bayern, Kane converted a penalty in the 15th, tapped home in the 51st and set up Kingsley Coman for the other in the 43rd.
The England captain's league-leading 11 season goals are two more than the entire Union team has managed in their nine games.
Kane's second made Bayern the first team from Europe's top five leagues to reach 50 goals in all competitions this term.
"Every game we play we dominate. We score as a team and defend as a team. Another clean sheet is also great," Kane told Sky TV.
"It was a really good performance. It wasn't easy but we started really well. Overall, a very strong performance."
Bayern moved three points clear at the top ahead of Leipzig, who had led through Benjamin Sesko in the 27th minute before Maximilian Beier levelled three minutes later and set up Serhou Guirassy's winner in the 65th for injury-ridden Dortmund.
It meant Dortmund maintained their 100 per cent home record this season and rose to fifth, seven points behind leaders Bayern.
Victory was sweet for beleaguered coach Nuri Sahin and his players who had previous crashed 5-2 at Real Madrid in the Champions League, 2-1 at Augsburg in the Bundesliga and 1-0 at Wolfsburg in the German Cup.
Leipzig's unbeaten Bundesliga run ended after 19 matches overall.
Frankfurt rose to third, another three points behind. They led 4-0 after 32 minutes and scored three more within eight second-half minutes after Bochum had pulled back two. Huge Ekitike scored twice while Omar Marmoush had a goal and two assists.
Elsewhere, promoted Holstein Kiel landed their first ever Bundesliga victory when a Patrick Erras header lifted them to a 1-0 win over Heidenheim.
Wolfsburg were held 1-1 by Augsburg, while Jackson Irvine's St Pauli enjoyed a second victory this season, 2-0 at Hoffenheim.
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