Salah put his side ahead in the first half, firing beyond keeper Joe Hart after the Hammers were caught out by a quick counter-attack.
The Reds doubled their lead soon after when Joel Matip slotted home from a corner.
Manuel Lanzini’s deft finish briefly gave the hosts hope but Alex Oxlade-Chamberlain’s first Premier League goal for Liverpool restored their two-goal advantage before Salah’s powerful finish sealed the win.
Liverpool’s fifth Premier League win of the season keeps Jurgen Klopp’s side sixth in the table, while West Ham are 17th and just one point above the relegation zone.
West Ham’s points total of nine after 11 games matches their total over the same period in 2010-11 when they were relegated from the top flight.
An inconsistent start to the season had threatened to end Liverpool’s title challenge before it had even started.
The Reds won just three of their opening nine games and a thumping 4-1 defeat at Tottenham on 22 October left them down in ninth, 12 points behind leaders Manchester City.
Liverpool’s attacking play has been outstanding at times this season but during those early games they lacked the clinical touch in the final third to round it off.
However, successive 3-0 wins against Huddersfield in the Premier League and then Maribor in the Champions League in recent weeks suggested that had perhaps been found.
