Michael Olise pressured Trevoh Chalobah into an own goal with 20 minutes gone, before Kane won and converted a penalty seven minutes later.

Cole Palmer finished off a superb team counter-attack just two minutes later to bring Chelsea back into the game.

But Kane stepped up again midway through the second half to wrestle control back Bayern's way.

England captain Kane says facing Premier League sides gives him extra motivation to "play better", and Chelsea were on the receiving end as he climbed up to 10 goals in just six games this season.

Bayern captain Manuel Neuer, the last survivor from the 2012 Champions League final between the sides, won by Chelsea at the same venue, brought up his 100th win in the competition. He now trails just Cristiano Ronaldo, Thomas Mueller and Iker Casillas.

Bayern have now won their past 22 Champions League openers dating back to a 2002 loss to Spain's Deportivo La Coruna.

Chelsea coach Enzo Maresca restored Palmer and three others to the starting line-up, having copped criticism for resting players in Saturday's limp 2-2 draw at Brentford.

Bayern had won five from five to start the season but were caught off guard early by the visitors' intensity, with Chelsea pinning the hosts back.

Bayern caught their breath and created some pressure of their own before breaking through when Chalobah failed to deal with an Olise cross, turning it into his own goal.

The hosts were soon two up as Kane struck from the spot.

Moises Caicedo gave away the penalty with an awkward tackle in the box but helped Chelsea hit back immediately, playing a clever one-two on the break, allowing Palmer to slam home.

Bayern came to life 10 minutes into the second half, with Konrad Laimer, Kane and Olise all having efforts saved in quick succession.

Kane broke through shortly after, pouncing on a poor Malo Gusto back-pass before sliding the ball into the far corner.

The 32-year-old was taken off to a standing ovation in stoppage time, with Chelsea loanee Nicolas Jackson coming off the bench to make his Champions League debut against his parent club.