Trent Alexander-Arnold and Roberto Firmino scored the vital goals as Liverpool made it six wins out of six this season - and 15 league wins in a row - to restore their five-point lead at the top of the table.

Liverpool boss Juergen Klopp told Sky Sports: "It was a really good performance and we scored two wonderful goals.

"It was an exciting game and it was intense and you will never win at Chelsea without putting a proper shift in, and I think we deserved the three points."

"We didn't deserve to lose, possibly could have won," Chelsea manager Frank Lampard said.

"I don't want to sound naive but performance wise I thought we were the better team, we kept pushing."

Arsenal climbed to fourth after a 3-2 win over Aston Villa, despite playing almost an hour with 10 men.

Manchester United's poor start continued as they were beaten 2-0 at West Ham while Crystal Palace drew 1-1 with Wolves.

Liverpool were 2-0 up at half-time through a superb free kick from Alexander-Arnold and a header from Firmino.

Chelsea had a goal ruled out for offside but reduced the deficit in the second half when N'Golo Kante fired the ball into the top corner with 20 minutes to go.

That sparked a frenzy of Chelsea attacks but they couldn't find the equaliser and Liverpool moved clear again at the top while the hosts slipped to 11th.

Ten-man Arsenal twice came from behind to beat Aston Villa and take a place in the top four.

John McGinn put Villa in front and though Ainsley Maitland-Miles was sent off before half-time, Arsenal equalised through Nicolas Pepe.

Wesley restored Villa's lead almost immediately but Calum Chambers levelled and Pierre-Emerick Aubameyang won it for Arsenal with six minutes to go.

Andriy Yarmolenko and Aaron Cresswell scored the goals as West Ham moved up to fifth with a well deserved win over United, who dropped to seventh after their second defeat in six matches.

United manager Ole Gunnar Solsjkaer bemoaned his side's inability to take their chances.

"(They had) two great finishes but of course we could have done better defending them and we should have, could have scored ourselves," he said.

And United suffered insult to injury as striker Marcus Rashford suffered a groin problem.

"We'll do a scan tomorrow to see how badly he's injured," Solskjaer said.

"I don't know how long he'll be out, I'm not a doctor. But he'll probably be out for a little while."

Former Manchester United captain Roy Keane said he was "shocked and saddened" by how bad his old team were in their 2-0 defeat at West Ham.

Keane, who won 13 major trophies during his spell at Old Trafford under Ferguson, said on Sky Sports: "I was shocked and saddened by how bad they were today.

"They were lacklustre, no quality, lack of desire, lack of leaders, lack of characters. It's a long way back for United but scary how far they've fallen."

Diogo Jota scored in the fifth minute of injury time to give Wolves a draw at Crystal Palace, despite having Romain Saiss sent off 17 minutes from the end.

Australian Associated Press