LONDON, Sept. 22 -- English Premier League leaders Liverpool maintained their perfect start to the season by holding off a second-half fightback to earn a 2-1 win at Chelsea on Sunday.

Trent Alexander-Arnold and Roberto Firmino scored the goals as Liverpool made it six wins out of six this season and have now collected 15 Premier League wins in a row, keeping their five-point lead at the top of the table.

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

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

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

Chelsea had a goal ruled out for offside when it was 1-0 and 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 equalizer and Liverpool moved clear again at the top while the hosts slipped to 11th, as pressure continues to mount of boss Frank Lampard.

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

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

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