Emre Can gave the Reds a deserved lead just before the half-four mark, Salah and Roberto Firmino added to the advantage after the break. Michail Antonio pulled one back for the visitors, but Sadio Mane restored the three-goal gap.
Salah has now bagged 23 goals, tying Tottenham Hotspur's Harry Kane for the Premier League lead.
Here's a look at the teams, via James Pearce of the Liverpool Echo:
It took the Reds just three minutes to muster their first major chance, as some nice passing between Salah and Firmino saw the former put goalkeeper Adrian to work for the first time.
Liverpool were all over the Hammers early, but Adrian was strong, denying Virgil van Dijk after his defenders gave away a corner.
Reds 'keeper Loris Karius also had to flash his talent, getting his fingers to a wonderful effort from Marko Arnautovic and pushing the ball onto the woodwork. Football writer Leanne Prescott was impressed:
The pace of the contest dropped after a quick first 15 minutes, but the Reds remained the better team, applying pressure in midfield and moving the ball well. Chances were rare, but when the hosts found another look on goal, they took the lead.
Adrian and his defenders blundered at a corner, and Can easily beat Patrice Evra to open the scoring. Per Bleacher Report's Matt Jones, the goalkeeper in particular was to blame:
Salah had a good chance to double the lead shortly after, but his header missed the target.
The half finished with the hosts on top and a nasty challenge from James Collins, who became the first man to receive a booking.
The pattern of the contest didn't change after the break, and just a few minutes into the second half, the Reds doubled their advantage. Salah bagged his 23rd goal of the campaign after a good pass from Alex Oxlade-Chamberlain.
Per Prescott, the provider deserved all the credit:
And there was more to come from the Reds, who feasted on a dejected defence after the second goal. Firmino also got his name on the scoresheet, courtesy of a great ball over the top from Can and a poor intervention from Adrian.
But just as West Ham seemed ripe for the slaughter, substitute Antonio made an immediate impact, taking a smart pass from Cheikhou Kouyate and beating Karius to make it 3-1.
Per OptaJoe, he enjoys going up against Liverpool:
Salah could have restored the advantage after a quick move down the wing, but his shot didn't trouble Adrian.
Mane eventually found the reassuring fourth goal, with his chip coming off the post before going in.
Liverpool's next outing will be at home against Newcastle United, while West Ham visit Swansea City.