The hosts burst out of the blocks and saw their early endeavour rewarded as Winston Reid bundled home inside 90 seconds and Diafra Sakho doubled their advantage soon after.
Raheem Sterling was able to pull one back for Brendan Rodgers’ visitors, who have now lost three of their opening five fixtures, but a poor clearance from Mamadou Sakho late on led to Morgan Amalfitano being teed up to seal the win for Sam Allardyce’s side.
Liverpool are now six points behind leaders Chelsea in the table, having played a game more, while the pressure on Allardyce, in front of his own fans at least, has lessened with a first home win of the season.
Liverpool needed a last-gasp penalty to beat Ludogorets on their UEFA Champions League return in midweek, but face a test of their top four credentials this season.
The Reds, runners-up last term, were expected to add to West Ham’s misery and inflict a third home loss of the season after Tottenham Hotspur and Southampton won last month.
Liverpool had Martin Skrtel restored following a three-match absence with a knee injury, but a defensive reshuffle was required after 22 minutes, by which time the visitors were already two down.
The source of the first goal was former Reds winger Stewart Downing, whose inswinging free-kick found James Tomkins at the back post.
Tomkins’ header back across the six-yard box was turned goalwards by Reid, whose header went in off Dejan Lovren.
Downing seemed determined to impress and danced around Steven Gerrard before Mark Noble darted from left to right and fed Diafra Sakho.
The Senegal forward, a summer recruit from Metz, burst into the area and had the audacity to lob the ball over Simon Mignolet into the far corner for his third goal in three games.
Aaron Cresswell then tried his luck from 25 yards and Mignolet turned the ball round the post.
The closest Liverpool came to the Hammers goal in the opening 20 minutes was when Mario Balotelli attempted to block an Adrian clearance and tangled with the goalkeeper, who kicked out before facing off with the striker. Both men were booked.
A frustrated Rodgers hauled off Javier Manquillo for Mamadou Sakho and switched to a back three in an attempt to wrest some of the initiative from Cheikhou Kouyate and Alex Song in midfield.
Liverpool struck back when Balotelli pulled down a Jordan Henderson cross from the left and saw his shot blocked by Cresswell. The ball ricocheted to Sterling, who drilled a low first-time volley into the far corner.
West Ham continued to press forward and Mignolet turned a Enner Valencia free-kick round the post.
Lovren required lengthy treatment after colliding with his team-mate Mamadou Sakho. He initially appeared groggy but returned following a change of shirt, with a heavily bandaged head and after a consultation with the tunnel doctor in compliance with Premier League concussion rules.
Mignolet saved from Valencia as the Hammers’ bombardment continued.
Adam Lallana replaced Lucas at half-time and tried to tee up Sterling, who dragged his shot wide.
Liverpool exerted some more pressure, with Fabio Borini and Balotelli each twice finding shooting space without really testing Adrian.
As the visitors pushed forwards, gaps in their defence became evident.
Diafra Sakho was unable to punish a Skrtel lapse as he lifted the ball over, but a third West Ham goal came when they broke and Downing threaded the ball through for substitute Amalfitano to score.