Volkswacht Bodensee - Liverpool humbled again as Arsenal down Bayern in Champions League

Holders PSG saw off Tottenham in an eight-goal thriller at the Parc des Princes and Kylian Mbappe scored four times in a Champions League match for the first time as Real Madrid beat Olympiacos 4-3.

Beleaguered English champions Liverpool suffered a ninth defeat in 12 games in all competitions as they crumbled against PSV.

Liverpool conceded in just the sixth minute when Virgil van Dijk inexplicably handled the ball while appealing for a foul from a corner, with Ivan Perisic dispatching the resulting penalty into the corner.

Slot's struggling side hit back quickly as Dominik Szoboszlai slotted in after visiting goalkeeper Matej Kovar could only parry Cody Gakpo's shot.

PSV came out firing after the interval and restored their lead when Mauro Junior's brilliant pass was steered in expertly by Guus Til.

The hosts' latest humiliation, after a 3-0 home loss to Nottingham Forest at the weekend, was confirmed as Couhaib Driouech twice took advantage of calamitous defending to score late on.

Premier League leaders Arsenal maintained their 100-percent record in the competition this season by ending Bayern's, taking top spot in the 36-team table from the Bavarians with a 3-1 success.

Bayern fell behind at the Emirates in the 22nd minute when Jurrien Timber flicked Bukayo Saka's corner past a flailing Manuel Neuer.

But 17-year-old Lennart Karl became the first player to score against Arsenal in the Champions League this season, firing home from an excellent volleyed pass by Serge Gnabry.

Noni Madueke put Arsenal back in the lead in the 69th minute, though, before Gabriel Martinelli tapped into an empty net after Neuer raced out of his goal and was beaten to the ball near the halfway line.

"It's an incredible statement, but we know the work we put in," Madueke told TNT Sports. "We go into these games with every confidence that we are going to win."

- Vitinha inspires PSG comeback -

PSG bounced back from their loss to Bayern earlier this month as Vitinha scored a hat-trick in a 5-3 victory over Tottenham.

Spurs, as they did against PSG in the UEFA Super Cup in August, struck first when Richarlison nodded in from close range to finish off a fine team move.

But the home side equalised on the stroke of half-time courtesy of a rasping long-range drive from Vitinha following a short corner routine.

PSG fell behind again less than five minutes into the second half as Randal Kolo Muani hammered home a volley to score his first Spurs goal since joining on loan from the Ligue 1 giants.

Luis Enrique's men wasted no time in responding as Vitinha curled in another brilliant strike from the edge of the box, before Fabian Ruiz put them in front for the first time after Cristian Romero gave the ball away.

Willian Pacho appeared to have put the game to bed, but Kolo Muani drilled in to give Tottenham renewed hope against his parent club.

PSG finally secured the three points through a Vitinha penalty in the 76th minute.

- Four-goal Mbappe -

Mbappe ran riot as Real Madrid moved into fifth place and snapped a three-game winless streak.

Olympiacos grabbed a surprise early lead when Chiquinho finished off a quick passing move with a powerful shot past stand-in Madrid 'keeper Andriy Lunin.

But Mbappe levelled midway through the first half and scored his second just two minutes later, heading Arda Guler's cross into the bottom corner.

He completed his fifth Champions League treble after racing clear on goal.

Mehdi Taremi pulled one back for the Greeks early in the second period but Mbappe quickly restored Real's two-goal advantage.

Olympiacos' Ayoub El Kaabi halved the deficit but the 15-time European champions held on.

Last season's runners-up Inter Milan missed out on the chance to go second in the table as Jose Maria Gimenez's injury-time goal snatched Atletico Madrid a 2-1 win at the Metropolitano.

Atalanta climbed to 10th in the table with an impressive 3-0 triumph at Eintracht Frankfurt, while David Luiz scored as Pafos held Monaco to a 2-2 draw in Cyprus.

FC Copenhagen held off a late Kairat Almaty fightback to post their first win with a 3-2 victory in Denmark.

C.Kreuzer--VB