Leverkusen’s win meant the perennial German champions started seven points behind but Kane settled nerves by netting after two minutes, tapping home a pass from Leroy Sane.
Bayern lost midfielders Leon Goretzka and Joshua Kimmich to flu just hours before the match and had only five outfield players on the bench but dominated a listless Stuttgart.
“Today was intense,” Bayern coach Thomas Tuchel said of his team’s injury crisis, revealing that “I tried to stay calm and keep my distance on the sidelines to give the players a bit more confidence. “
“Today is very good, it’s not over yet, we have some other game. “
Bayern scored two more goals for offside in the first half, but Kane scored a brace early in the second, with a header from very close range from a free kick.
Kim Min-jae was next to score, heading in from another set piece for his first goal in Bayern colours, sealing the game for the home side.
Kane told DAZN that it was “probably our most productive performance of the season,” saying that “everyone who came in did really well. We’ll need him for the whole season. “
Bayern are four points behind Leverkusen and have a game in hand, against Union Berlin, who are in 15th place in January.
Kane’s brace saw him score 20 league goals in 14 games this season, four ahead of Stuttgart’s Serhou Guirassy, who has been silenced by Bayern’s stingy defence.
Earlier on Sunday, Nigeria striker Victor Boniface scored and laid on two assists as Leverkusen beat Frankfurt 3-0, continuing his side’s hopes of a maiden Bundesliga title.
Before the match, Leverkusen fans released a huge Christmas wish list, asking the club to make their dreams of making a name in the Bundesliga come true.
“We’ve won nothing yet. After half a year nobody wins anything, especially not a league title,” Leverkusen midfielder Granit Xhaka said to DAZN.
“We’ve got another game midweek and then we go on holiday, where we need to be careful what we do. Then we’ll come back and step on the gas ahead of the rest of the season.”
Leverkusen, unbeaten thanks to Xabi Alonso, have won 21 games and drawn 3 of 24 games in all competitions this season.
Boniface squeezed a low shot under Kevin Trapp to open the scoring 14 minutes in.
The Nigerian then set up Jeremiah Frimpong’s goal early in the second half, his shot bouncing off Trapp and he scored perfectly for the Netherlands to head home.
The 22-year-old, who is sure to be chosen for Nigeria’s Africa Cup of Nations bid in January, helped seal the result by putting Florian Wirtz in the box for Leverkusen’s third goal.
Wirtz, who was again superb while pulling the strings in midfield, hit the crossbar with 10 remaining.
Frankfurt have won just one of their last eight games in all competitions: the unexpected 5-1 home win over Bayern last Saturday.
Freiburg’s Michael Gregoritsch and Roland Sallai came off the bench to secure a 2-0 home win over 10-man Cologne.
Tenacious but outclassed, Cologne fought hard but were reduced to 10 men with just over an hour to go when Jeff Chabot swept Lucas Hoeler’s legs and picked up a second yellow card.
Hoeler replaced Gregoritsch and shortly afterwards the 1. 93m Austrian gave Freiburg the lead.
Gregoritsch was the first to lose the ball in the Cologne box and set his team on course for their seventh win of the season.
Gregoritsch has now scored in his past league three games, having broken a goal drought which dated back to April.
“I just keep scoring,” a thrilled Gregoritsch told DAZN.
“I’m in the right position at the right time. . . Of course, my self-confidence is getting back a bit. “
Sallai, who also signed for Gregoritsch, scored in the 5th minute of stoppage time to seal the result.