Bayern profited from defending champions Bayer Leverkusen's 2-2 draw in Leipzig on Saturday, as Florian Wirtz struck the post three times and the visitors were left to rue Edmond Tapsoba's late own goal.
Kane opened the scoring early with a right-footed shot past Freiburg goalkeeper Noah Atubolu after turning inside Philipp Lienhart with a good first touch.
It was his first league goal from open play since November 22, when he also scored two penalties. He had only scored two spot kicks in the six Bundesliga games since then.
But Bayern coach Vincent Kompany pointed to what else Kane brings to the team, including his defensive work.
"He also plays an important role with his character," Kompany said. "He's going to give his all to be successful this year, and we're using that, too."
Kim Min-jae got Bayern's second after the break, before Matthias Ginter pulled one back with a header in the 69th, but it was too little too late for Freiburg.
Bayern's tally of 48 points after 19 rounds is their best return for nine years as they seek to regain the title.
Borussia Dortmund ended their four-game losing streak across all competitions in their first game since firing coach Nuri Sahin, but there was little celebration.
The 10-man team had to defend doggedly to preserve a 2-2 draw with Werder Bremen, who came from two goals down after Nico Schlotterbeck had been sent off for Dortmund.
Former Dortmund players Leonardo Bittencourt and Marvin Ducksch scored to draw the visitors level.
Dortmund Under-19s coach Mike Tullberg took interim charge while the club searches for a successor to Sahin.
Stuttgart, last season's runners-up, lost in Mainz 2-0, and Augsburg enjoyed a 2-0 home win over relegation-threatened Heidenheim.
Borussia Mönchengladbach defeated last-placed Bochum 3-0 in the late game.
