England skipper Kane marked his 100th Bundesliga appearance for Bayern Munich by scoring his 102nd goal, joining in a 6-1 rout of RB Leipzig that also featured Luis Diaz netting a hat-trick.
After a mixed start to the season, Bayern moved to their familiar position at the top of the table as they outclassed their opponents at Allianz Arena.
It was already 4-0 by the time England captain Kane marked his century of outings in the league with a customary goal, a simple finish from Nathaniel Brown's pass.
Diaz scored in the 12th, 47th and 69th minutes, with Aleksandar Pavlovic and Michael Olise also on target in a statement performance that ended with an added-time consolation from Andrija Maksimovic.
Three points saw them overtake rivals Borussia Dortmund on goal difference, with Niko Kovac's side giving up ground with a goalless draw at strugglers Union Berlin.
In LaLiga, Barcelona stretched their perfect record to nine wins from nine as they swept aside hosts Real Betis 5-2.
Yamal got the ball rolling in the 10th minute with his eighth of the season, a quite stunning left-foot strike after bamboozling a Betis defender, and the goals just kept flowing thereafter.
Diego Gomez equalised, Rodri and Gabriel Jesus rebuilt the lead and Abde Ezzalzouli hit back.
Facundo Bernal's 54th minute red card stacked the deck against Betis at 3-2 down, with Eric Garcia and Dani Olmo adding the gloss.
Second-placed Atletico Madrid followed their midweek Champions League win over Manchester United with a 1-0 win at Espanyol. They left it late to bank the points, Alex Baena grabbing an 89th-minute winner.
Inter Milan's strong start in Serie A continued as they came from behind to beat Bologna 3-1. Tomasso Pobega put the pacesetters on the back foot before a towering header from Marcus Thuram equalised before the break.
Substitutes Carlos Augusto and Ange Bonny came off the bench to complete the turnaround in the second half, leaving the Nerazzurri three clear on 19 points after seven matches.
Paris St Germain made it six consecutive wins across all competitions with a 3-1 win at Strasbourg.
A PSG side showing eight changes from the midweek trouncing of Manchester City slipped behind to Gio Reyna and missed a penalty though Ousmane Dembele but safely negotiated the comeback.
Illia Zabarnyi levelled, Dembele made amends and Desire Doue earned the third in added time.
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