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Darwin Nunez scored a fine goal as Liverpool saw off West Ham to extend their unbeaten run to 18 games in all competitions.
Mohamed Salah gave Liverpool the lead against the run of play with a penalty after he was brought down by Nayef Aguerd.
Jarrod Bowen levelled for West Ham with an excellent stooping header to meet Vladimir Coufal's cross.
Soon after Curtis Jones had a goal ruled out for Liverpool for offside.
Nunez put them ahead with a difficult hooked volley from Alexis Mac Allister's clipped ball over the top.
The Hammers played well in stages but never created a clear-cut chance to equalise.
And Diogo Jota sealed the points when he pounced from close range to turn home Virgil van Dijk's header.
West Ham boss David Moyes has now lost 24 Premier League games against Liverpool, a joint record for a manager against one team, level with Harry Redknapp against Manchester United.
Both sides were in Europa League action on Thursday - and Moyes and Jurgen Klopp made nine changes each from those games.
A victory would have seen West Ham equal their best start to a Premier League season, matching their haul of 13 points from six games in 1999-2000.
They started the brighter and Alisson needed to get down low to make an excellent save from Tomas Soucek's header towards the bottom corner.
Michail Antonio headed wide, and Salah's opener - a penalty he won himself after a quick counter - was the Reds' first real chance.
Salah is the fifth player to either score or assist a goal in each of his team's first six games of a Premier League season, after David Beckham, Thierry Henry, Sergio Aguero and Erling Haaland.
The Reds improved after that and Van Dijk, back from his Premier League ban, Mac Allister and Salah all missed the target.
But then West Ham were level - as Bowen dived in bravely to head Coufal's cross past Alisson, via the inside of the post.
Bowen is the first player to score in West Ham's opening four away games in a top-flight campaign since Vic Watson in 1929-30.
But once Nunez expertly poked a volley past Alphonse Areola, the Reds never looked back.
The win was secured from a corner routine. Andy Robertson found Van Dijk, who headed down and Jota could not miss from inside the six-yard box.
Liverpool look, not back to their best, but a lot better than they did for the majority of last season. Their 17-game unbeaten run in the league is a full 10 games longer than any other team's current run.
They are second in the table, only behind Manchester City - a situation you wonder if we will get used to as the season goes on.
