Paris Saint-Germain beat Liverpool 4-1 in a penalty shootout to advance to the Champions League quarterfinals after winning a rip-roaring last-16 second-leg match at Anfield 1-0 on Tuesday thanks to a goal from Ousmane Dembélé.

After the tie had finished 1-1 in the aggregate, PSG goalkeeper Gianluigi Donnarumma saved spot kicks from Darwin Núñez and Curtis Jones, while the visitors converted all their efforts.

PSG will meet either Aston Villa or Club Brugge in the quarters, with Villa taking a 3-1 lead into Wednesday's second leg.

Dembele stunned the Anfield crowd with his 12th-minute goal against the run of play. Ibrahima Konaté slid in to block Bradley Barcola's effort but pushed the ball away from goalkeeper Alisson in the process, and Dembélé needed only to knock it into an empty net.

The goal was the earliest Premier League-leading Liverpool had conceded at Anfield in the Champions League since September 2017 against Sevilla.

Arne Slot's team played considerably better than a week earlier -- when it needed a last-gasp goal from substitute Harvey Elliott after the Parisians had dominated -- and Reds talisman Mohamed Salah had a shot blocked on the goal line by Nuno Mendes in the game's first few minutes.

Donnarumma was forced into making an early diving save to keep out a shot from Konaté, but both sides spurned chances in a nervy game that had fans on the edge of their seats.

Liverpool parked themselves in PSG's territory for much of the second half of normal time and had a goal from Dominik Szoboszlai disallowed for offside in the buildup early in the second period.

They kept Donnarumma busy in the dying minutes, with the keeper parrying away ball after ball fired into the box, but it was Dembélé who unleashed what looked like the winner in extra time before Alisson made a dramatic diving save to push the ball wide with his fingertips.

PSG were rock solid under pressure in the shootout, with Vitinha, Gonçalo Ramos, Dembélé and Désiré Doué finding the net. Liverpool got off to a good start with Salah slamming his effort home, but Núñez and Jones had tame efforts comfortably stopped by Donnarumma.

The Liverpool boss was magnanimous in defeat and even had words of praise for his beaten side.

"I think it was the best game of football I've ever been involved in," he said.

"We ran out of luck maybe after last week. After 90 minutes we played the perfect game except for not scoring."

History was not on the Parisians' side on Tuesday, as they became just the fourth of 28 teams to progress after losing the first leg at home in a Champions League knockout tie.

"Both of the teams deserve to go to the next phase," said PSG boss Luis Enrique.

"They played better than us here, but I think my team at Anfield, in a special stadium showed great personality and character.

"We tried to play our best, but it was difficult as they're so intense. Both teams deserve to qualify."

The thousands of travelling fans, many of them shirtless despite the chilly temperature, were not daunted by their team's odds, as they danced and sang until the final whistle.

Liverpool have little time to rest ahead of Sunday's League Cup final against Newcastle United.

"It's part of football," Liverpool captain Virgil van Dijk said of Tuesday's defeat. "I said to the guys, 'Obviously, you can be disappointed because we're out of the competition, but chin up and get ready for the next challenge, a beautiful one on the weekend.'"