With 31 goals in 26 league games since arriving from Spurs in the summer, Kane overtook German legend Uwe Seeler, who scored 30 goals for Hamburg in 1963-64.
Musiala also had an assist in the win, which keeps Bayern’s slim hopes of defending the Bundesliga title alive, moving them seven points behind Bayer Leverkusen, who play at Freiburg on Sunday.
“We are staying in it. We worked hard to get ourselves some opportunities and we took them,” said Bayern captain Manuel Neuer, praising “difference makers like Jamal on the pitch.”
The goalkeeper was however disappointed his side had conceded two goals against last-placed Darmstadt, saying: “We all need to work on it.”
Darmstadt stunned Bayern after 28 minutes, Tim Skarke taking advantage of some sleepy defending by Eric Dier to score and give the home side hope of an incredible upset against the German champions.
Kane would however drag Bayern into the lead before half-time, assisting Musiala’s 36th-minute goal before scoring one of his own, rising high to head in a Joshua Kimmich chip in first-half stoppage time.
Musiala added another midway through the second half when he collected a Thomas Mueller throw-in and danced through the box before shooting between the goalkeeper’s legs.
As he did last week, Serge Gnabry scored moments after coming off the bench to seal the win.
Bayern’s Mathys Tel and Darmstadt’s Oscar Vilhelmsson both scored in stoppage time.
• Stuttgart sizzle –
In Saturday’s late game, Stuttgart continued their remarkable turnaround this season, Serhou Guirassy scoring again in a 3-0 win over neighbours Hoffenheim.
Third from bottom last season and needing to win a play-off to stay in the first division, third-placed Stuttgart have rocketed up the table this year and now have one hand on a top four spot and a return to the Champions League.
Enzo Millot’s 16th-minute goal broke Hoffenheim’s resistance and Guirassy scored just before half-time, his 22nd league goal of the season after just 20 games.
Jamie Leweling scored to seal the win with 20 minutes remaining to seal Stuttgart’s first win in Hoffenheim for over a decade.
In the German capital, Union Berlin beat Werder Bremen 2-1 thanks to a commanding performance from US midfielder Brenden Aaronson, on loan from Leeds.
Aaronson, who was surprisingly left out of the US squad this week, had a hand in two goals in three second-half minutes to give Union the upper hand.
The 23-year-old laid on Yorbe Vertessen’s 50th-minute goal, before creating and scoring one of his own with some superb dribbling shortly after.
Mitchell Weiser pulled one back for the visitors but Union held on, recording their fifth win in seven home matches under coach Nenad Bjelica.
“It’s been the toughest year of my life,” Aaronson told reporters after scoring his second goal in Union colours.
“Going from Leeds and then not playing much here, it’s mentally a battle all the time, staying confident.”
Augsburg came from a goal down to beat a 10-man Wolfsburg 3-1 away from home, their fourth-straight league win taking them to seventh on the table.
Wolfsburg’s Patrick Wimmer scored after just nine minutes but was sent from the field in tears just before half-time for a last-man foul, with Augsburg’s Arne Maier scoring from the ensuing free-kick.
Kristijan Jakic scored a second-half double to seal the win, piling more pressure on Niko Kovac’s Wolfsburg who have won just one game in 15.
Mainz won 2-0 at home against Bochum to keep their hopes of avoiding relegation alive. Mainz moved past Cologne, who were thumped 5-1 by Leipzig on Friday, into 16th, the relegation playoff spot.
Promoted Heidenheim drew 1-1 at home with Borussia Moenchengladbach to collect another valuable point and go 10 clear of the relegation spots in their first season in the top division.
AFP