Liverpool snatched a late winner to beat Paris Saint-Germain away 1-0 in the first leg of their heavyweight Champions League last-16 tie on Wednesday, while Bayern Munich took charge with a 3-0 win over German rivals Bayer Leverkusen.

French league leaders PSG dominated at the Parc des Princes but couldn't make their superiority count and Harvey Elliott struck three minutes from time after replacing Mohamed Salah with Liverpool's only shot on target.

Khvicha Kvaratskhelia had a goal ruled out for offside in the first half but Arne Slot's side defended resolutely to keep PSG at bay and are in a strong position to advance to the quarterfinals going into next week's second leg at Anfield.

Liverpool goalkeeper Alisson Becker made several crucial saves as PSG had 28 attempts on goal but could not replicate the finishing that had allowed them to score 21 goals in their last five Champions League outings.

"It was probably the performance of my life," Alisson told TNT Sports.

"To go away with a win over here was probably a bit more than we deserved," added Slot.

If Liverpool finish the job at home next Tuesday, they could face Aston Villa in the quarterfinals, but PSG coach Luis Enrique said his side will have "nothing to lose".

"We deserved to win clearly, we created a lot of chances," said the Spaniard. "Football is unfair many times and you have to accept that."

Harry Kane scored twice as Bayern closed in on the last eight with a first win over Xabi Alonso's Leverkusen in seven matches.

The England captain headed in Michael Olise's superb cross to give Bayern the lead at the Allianz Arena.

Jamal Musiala added a second early in the second half when Leverkusen goalkeeper Matej Kovar let an innocuous delivery into the box from Joshua Kimmich slip from his grasp.

Bayern lost Manuel Neuer to injury before the night went from bad to worse for Leverkusen, who had Nordi Mukiele sent off.

Kane rounded off the scoring from the penalty spot following a VAR review after he was impeded by Edmond Tapsoba.

"It was a really big step in the right direction. We've struggled against this side over the last couple of years," Kane told DAZN.

A downbeat Alonso admitted it would take a remarkable turn of events for Leverkusen to overturn the deficit.

"In football we've seen big miracles quite often and we almost need one," he said.

NARROW BARCA ADVANTAGE

Barcelona edged past Benfica 1-0 in Lisbon thanks to Raphinha's second-half strike despite playing most of the game with 10 men.

Teenage defender Pau Cubarsi was sent off midway through the first half for a foul as the last defender, but Barcelona clung on and Raphinha drilled home after 61 minutes to give the five-time European champions a slim advantage.

"I said to the (team) chapeau, I'm very proud," said Barcelona coach Hansi Flick.

"After the 22nd minute with 10 players it was not easy, and this is a big win."

Inter Milan seized control of their tie against Feyenoord as Marcus Thuram and Lautaro Martinez scored in a 2-0 win in Rotterdam.

France striker Thuram hooked in a cross from Nicolo Barella slightly against the run of play late in the first half, with Lautaro Martinez lashing in a second on 50 minutes.

"We had to suffer a bit tonight but we didn't have to for long," said Inter coach Simone Inzaghi.

"We were together when we needed to be. We know the challenges that the second leg will bring, but I am very happy."

Feyenoord knocked out Inter's city rivals AC Milan in the play-off round but have since changed coaches, with former Arsenal and Manchester United striker Robin van Persie returning to take charge of his hometown club. (AFP)

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