Fresh from scoring his eighth league hat-trick last week, Kane created the opener after 28 minutes, floating in a lovely chip for Serge Gnabry to head home.
Luis Diaz, who missed a sitter just two minutes in, made up for his mistake by adding Bayern’s second by slamming the ball through a crowded penalty box in first-half stoppage time.
Having put six goals past RB Leipzig a week ago, Bayern looked on track for another thumping win when Michael Olise wrong-footed the Augsburg defence to cooly score his side’s third in the 48th minute.
The home side pulled one back after 53 minutes however, Kristijan Jakic cutting the deficit with a controlled strike.
With minutes left, Mert Komur threaded the ball into the corner to give the hosts belief of an unlikely comeback.
The match continued into a 10th minute of stoppage time as Bayern held off their Bavarian rivals.
Late collapse for Leverkusen
Bayer Leverkusen let a two-goal lead slip to draw 3-3 at 10-man Werder Bremen, denying new coach Ten Hag his first league win in charge.
Leverkusen were 3-1 ahead and a man up after Patrik Schick’s Panenka penalty midway through the second-half, his second of the game.
Bremen were reduced to 10 men after Niklas Stark was shown a second yellow for the foul which led to the spot-kick.
But Leverkusen let Bremen back into the match when goalkeeper Mark Flekken advanced out of his area and misjudged a long ball, allowing Isaac Schmidt the easiest of finishes.
Bremen continued to attack and snatched a point in the fourth minute of stoppage time, Karim Coulibaly volleying in after the ball bounced off the crossbar.
Coulibaly, 18, is Bremen’s youngest ever goalscorer in the Bundesliga.
The result puts some early pressure on Ten Hag who is trying to weave together a team full of new recruits, while reviving his own reputation after a poor end to his Manchester United stint.
“There were too many simple mistakes from us… we did dumb things and gave the game away,” Tillman told DAZN.
Despite the disappointment, the draw kept Leverkusen’s remarkable away run alive, with the club unbeaten on the road in the league since May 2023.
“(It is) hard to accept. We have to improve very quickly. Obviously, this is not a good situation,” Schick said.
Elsewhere, new Eintracht Frankfurt winger Ritsu Doan scored a brace and added an assist as his side cruised to a 3-1 win at Hoffenheim.
Japan winger Doan, who arrived from Freiburg in the summer, netted Frankfurt’s opener on 17 minutes with a superb curling effort from well outside the box.
Doan doubled up 10 minutes later, tapping in a Jean-Matteo Bahoya pass on the break, before laying on an excellent pass for Can Uzun to score Frankfurt’s third.
Stuttgart beat Borussia Moenchengladbach 1-0 at home thanks to a late header from Chema Andres, just hours after striker Nick Woltemade’s departure to Newcastle was made official.
The German Cup holders were sluggish but grabbed the three points when Andres headed in with 79 minutes played after some poor marking by the Gladbach defence.
RB Leipzig bounced back from last week’s drubbing at the hands of Bayern, winning 2-0 at home against Heidenheim thanks to goals from Christoph Baumgartner and new striker Romulo Cardoso.
