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The England striker scored Bayern's second goal with a 27th minute penalty after an own goal by Chelsea's Trevoh Chalobah had put the hosts in the lead in the 20th.

Chelsea briefly rallied, with Cole Palmer pulling one back just two minutes later, but Kane, who has already scored five goals in three Bundesliga matches so far, struck again with a clinical low finish in the 63rd to settle the hosts' nerves.

Despite a quiet second half, Palmer put the ball in the net again in the 90th but his effort was offside.

Bayern, which crushed Hamburg SV 5-0 in the Bundesliga, continued its unbeaten run across all competitions while Chelsea, unbeaten in the Premier League, tasted defeat for the first time this season.