All four goals came in the second half in East London as the visitors claimed their second victory in a week in the capital.
Liverpool move above Leicester City in the league table after the Foxes' 3-1 loss to Leeds, whilst the result leaves the hosts in 5th place.
Story of the match
Divock Origi came into the Liverpool side in place of the injured Sadio Mane and had an early sight of goal when he was slipped in-behind by Xhedran Shaqiri, but his effort from a tight-angle sailed well wide of the near post.
West Ham had their first real chance halfway through the first half after some good play from Said Benrahma set up Pablo Fornals on the edge of the box, but his deflected shot was headed off the line by Andrew Robertson.
It was what you would expect from Liverpool in the first half. When they had the ball, they kept it well, but they struggled to break down the blunt West Ham backline and were unable to forge a decisive final pass.
There were limited attacks from either side until the last five minutes of the half. Michail Antonio, who was isolated up top for the majority of the first half, had a half-chance for the Irons when he met a deep cross from the left, but his tame header was gathered by Alisson.
Thiago Alcantara - in a more advanced midfield role compared to his first few appearances for the Reds - threaded a beautiful pass through to Origi on the stroke of half-time, but the Belgian's effort was poked wide at the near post as both sides left the pitch all-square.
Origi started the second half the same as the first - the 25-year-old was energetic for the Reds and nearly set Salah up for the opener when he surged down the left, breezed past Vladimir Coufal and his cross was met by Salah, but Aaron Cresswell tracked his run well and made a vital block to deny the Egyptian.
Origi was the man involved again - this time on the right after creating some room for himself in the box, but his driven effort evaded the pos and hit the side netting.
Much to the displeasure of James Milner, the 35-year-old was subbed off for Curtis Jones just before the 60-minute mark, however his anger soon turned to joy on the sidelines when the man who took his place set up Salah to score the opener.
Jones picked up possession on the halfway line and surged towards the Hammers box before laying it off the Trent Alexander-Arnold. The ball found its way back to Jones, with the midfielder finding Salah who then jinxed past Cresswell, cut onto his left and curled his shot into the top left corner.
The Egyptian then finished off a rapid counter-attacking move 10 minutes later to put his side two goals ahead.
Alexander-Arnold picked up the ball from a West Ham corner and set the Reds off on an expeditious attack. The 20-year-old sprayed a pass across the pitch for Shaqiri to run onto and he had time to weigh up his options, pick out Salah in the box and it was a touch of brilliance from Salah to control the ball and poke past Lukas Fabianski to grab his and Liverpool's second.
Wijnaldum made sure the game was out of sight for Liverpool with just over five minutes remaining after he finished off a brilliant team goal to add the Reds' third.
Substitute Roberto Firmino was at the heart of the move after his one-two with fellow substitute Alex Oxlade Chamberlain broke through the Hammers backline, and the Brazillian selflessly pulled it back for Wijnaldum to sweep into an empty net.
Dawson managed to pull one back for the home side with little time remaining after Cresswell's corner bounced through the box to the unmarked defender at the back-post, and Dawson had the simple job of tapping home into an empty net.
It only proved to be a consolation goal nevertheless as Jurgen Klopp's side make their way back to Merseyside with all three points.
Man of the Match
The Egyptian was a constant threat for Liverpool and despite not having many shooting chances, he was prolific when they came his way.
The 28-year-old scored a wonderful curling effort from the right corner of the box after smartly making his way past Cresswell, and he then grabbed his second of the match by finishing off a dazzling counter-attack after plucking the ball out of the air to poke past the 'keeper.