The Reds, now unbeaten in 16 matches on home soil in the top flight since last April, climb above Manchester United into second place with their fourth win in five matches.
Forward trio Mohamed Salah, Roberto Firmino and Sadio Mane were again on target, adding to Emre Can's headed opener a third of the way through the contest as the hosts kept their impressive run going.
Liverpool almost bagged the early goal they craved after Firmino picked out Salah, only for the Egyptian's shot to come back off the post with less than five minutes on the clock.
The elevation was almost perfect, but Karius got his fingertips to the ball and it hit the crossbar, while Pablo Zabaleta could only scuff a volley wide from the Hammers' next attacking move.
For all their intricate play in the opening half-hour, Liverpool's breakthrough goal arrived via a set piece as Can glanced the ball past Adrian with his head, moments after the West Ham stopper had produced two saves.
That was the Reds' 100th goal of the season in all competitions, and 101 did not look to be too far behind as Can curled a shot marginally wide and Salah headed over the bar when picked out at the back post.
West Ham were failing to truly make the most of their rare counter-attacking opportunities, though that nearly changed shortly before half time after Arnautovic got another shot away, this time going for power and forcing Karius into another smart save.
Three goals arrived in the opening 14 minutes of the second half, starting with Salah's composed finish through the legs of Aaron Cresswell and past Adrian after some good work from Alex Oxlade-Chamberlain to prod the ball through.
After seeing Mane kept out from close range, Firmino had less trouble as he poked the ball past the outrushing Adrian and had the simple task of rolling it into the unguarded net.
West Ham did attempt to make a contest of it, though, with the fourth goal of the day falling their way - Michail Antonio picking out the far corner from 10 yards just a minute after coming off the bench.
Adrian, at fault for Liverpool's third, redeemed himself somewhat by keeping out Firmino, Mane and Oxlade-Chamberlain in the space of a few minutes.
The post would come to the Hammers' rescue for a second time 17 minutes from time, with Mane unable to keep his composure after latching on to Oxlade-Chamberlain's through-ball.
Mane had better luck soon after, though, converting from a few yards out once spotted by Andrew Robertson at the end of another free-flowing move to complete the scoring.
LIVERPOOL (4-3-3): Karius; Alexander-Arnold, Matip, Van Dijk, Robertson; Milner, Can, Oxlade-Chamberlain; Mane (Moreno 87'), Firmino (Lallana 82'), Salah (Solanke 87')
WEST HAM UNITED (3-4-2-1): Adrian; Cresswell, Collins, Ogbonna; Zabaleta, Kouyate, Noble, Evra; Lanzini (Antonio 58'), Joao Mario (Rice 83'); Arnautovic (Hernandez 83')