Harry Kane was among the scorers as Bayern Munich beat Manchester United 4-3 in their heavyweight Champions League clash on Wednesday, while Jude Bellingham snatched a dramatic late winner for Real Madrid and Arsenal began their campaign with a big victory.

The meeting between German champions Bayern and a struggling United side was the biggest game of the opening round of matches in this season's competition and it did not disappoint.

Leroy Sane gave Bayern the lead at the Allianz Arena with a shot that squirmed through the grasp of United goalkeeper Andre Onana, and Jamal Musiala set up Serge Gnabry to make it 2-0 just after the half-hour mark.

Rasmus Hojlund pulled one back early in the second half with his first United goal, but shortly after Christian Eriksen was penalised for a handball in the box and Kane blasted in the resulting penalty.

Sane hit the post for the hosts before a crazy finish saw Casemiro reduce the deficit again, substitute Mathys Tel score Bayern's fourth, and Casemiro nod in another at the death to make it 4-3.

"A crazy finish," Kane said, after netting his fifth goal in six games for his new club.

"We lost a bit of concentration there in the last five minutes. Thankfully we were able to hold onto the lead."

Erik ten Hag's United team have now suffered three consecutive defeats in all competitions and lost four of their last five matches.

Thomas Tuchel's side are already in control of Group A, in which the other game saw Galatasaray come from two goals down to draw 2-2 with FC Copenhagen.

Goals from Mohamed Elyounoussi and Diogo Goncalves had the visitors in control in Istanbul but they then had Elias Jelert sent off and Galatasaray struck twice in the last four minutes of regulation time through Sacha Boey and Tete to earn a point.

In Madrid, Bellingham popped up from close range to score a 94th-minute winner as record 14-time European champions Real beat tournament debutants Union Berlin 1-0 in Group C.

Madrid's next game is away to Napoli, who won 2-1 against Braga in Portugal with Sikou Niakate's late own goal giving the Italian team victory.

Arsenal cruised to a 4-0 win over PSV Eindhoven in their first Champions League game since the 2016/17 season.

Bukayo Saka, Leandro Trossard and Gabriel Jesus all scored first-half goals in the rain in London and Martin Odegaard wrapped up the win after the break.

"It was a beautiful night after such a long time. It was great to see the atmosphere, the Champions League music. It was emotional before the game," Arsenal manager Mikel Arteta said.

Their Group B rivals Sevilla and Lens drew 1-1 in Spain, with Angelo Fulgini's free-kick earning the French side a draw after Lucas Ocampos headed the hosts in front.

Last season's beaten finalists Inter Milan needed an 87th-minute Lautaro Martinez equaliser as they came from behind to draw 1-1 at Real Sociedad in Group D.

In the same group Red Bull Salzburg missed one penalty but scored another in a 2-0 win away to Benfica in Lisbon. (AFP)