Their dominance continued after the break as Kane scored from the spot and assisted Mathys Tel before earning his first hat-trick for Bayern with minutes to go.
Kane’s excellent start with Bayern means he has now scored seven goals in five league matches as the defending Bundesliga champions sit top of the table.
Elsewhere in the Bundesliga, Marco Reus’ second-half goal earned Borussia Dortmund a 1-0 win over Wolfsburg while former Chelsea striker Timo Werner scored the only goal for RB Leipzig in their victory at Borussia Monchengladbach.
Hoffenheim won 2-0 at Union Berlin thanks to goals from Andrej Kramaric and Maximilian Beier, while Werder Bremen were 2-1 winners against Cologne. Davie Selke put the visitors ahead, but Rafael Borre and Justin Njinmah claimed the three points.
Ermedin Demirovic’s double earned 10-man FC Augsburg a 2-1 victory over Mainz, who had taken the lead through Ludovic Ajorque. Arne Engels was sent off in the 62nd minute, but Augsburg held on.
Joao Cancelo’s 89th-minute goal completed an amazing comeback by Barcelona as they scored three times in the final 10 minutes to beat Celta Vigo 3-2 in LaLiga.
Rafael Benitez’s Celta put in an excellent display and looked home and hosed as they went 2-0 up after 76 minutes when Tasos Douvikas added to Jorgen Strand Larsen’s excellent first-half goal.
But they succumbed to an incredible late rally that no one saw coming as Robert Lewandowski scored twice in four minutes before former Manchester City defender Cancelo won it with one minute of normal time left.
The comeback will paper over the cracks of what was a worrying display for Barca, who were cut open at will by a vibrant Celta side, but Xavi’s men go to the top of the table with the three points.
Benitez will be highly enthused by what he saw from his team, even if they are just one point above the drop zone.
Barcelona climbed above Girona, who continued their excellent start to the season with a 5-3 win over Mallorca, with goals coming from David Lopez, Artem Dovbyk, Ivan Martin, Yangel Herrera and Savio. Vedat Muriqi and Abdon Prats’ brace replied for Mallorca. Sevilla and Osasuna drew 0-0.
AC Milan drew level with city rivals Inter at the top of Serie A after a 1-0 win over Verona.
Rafael Leao’s early goal did the damage, though Inter can go clear later in the weekend.
Juventus missed the chance to go top after they slumped to a 4-2 defeat at Sassuolo.
The Bianconeri had claimed 10 points from an unbeaten start, but came unstuck at the Mapei Stadium as Sassuolo battled to a second league win.
Armand Lauriente, Domenico Berardi, Andrea Pinamonti and an own goal from Federico Gatti sealed the three points for Sassuolo. Juventus levelled twice through Matias Vina’s own goal and Federico Chiesa.
Nantes won an eight-goal thriller 5-3 against Lorient in Ligue 1.
Goals from Matthis Abline, Eray Comert, Mostafa Mohamed, Florent Mollet and Moses Simon did the damage, with Eli Kroupi, Romain Faivre and Tosin Aiyegun responding for the visitors in a topsy-turvy match.
Brest continued their excellent start to the season as Steve Mounier’s late effort gave them a 1-0 win over Lyon and top spot in the table.
Lazio and Monza shared a 1-1 draw in the late game in Serie A, while in LaLiga Almeria and Valencia drew 2-2.