The Hammers soaked up a lot of Liverpool pressure in the first-half and went close on a couple of occasions with Modibo Maiga spurning two golden opportunities to put the visitors in front.
But a Guy Demel own goal three minutes before the break, which he could nothing about after Jussi Jaaskelainen could only parry a Raheem Sterling effort in to his shins, gave Brendan Rodgers’ side a deserved lead to give them the upper hand.
And just two minutes into the second-half James Collins deflected a a Mamadou Sakho effort into his own net to double Liverpool’s lead and all but put the game to bed.
A Martin Skrtel own goal gave West Ham some hope of an unlikely comeback just after the hour, but Luis Suarez headed in his first ever goal against the Hammers to regain Liverpool’s two goal advantage with ten minutes remaining.
After Kevin Nolan was shown a straight red card for a studs up challenge on Jordan Henderson, Suarez saw his late effort take a generous deflection off defender Joey O’Brien and past Hammers stopper Jussi Jaaskelainen to complete the rout.
This victory, their second in a week after the 5-1 thrashing of Norwich City on Wednesday night, means Brendan Rodgers’ side are now second in the Premier League and four points behind leaders Arsenal.
Sam Allardyce’s West Ham, on the other hand, now only sit outside the bottom three on goal difference after Crystal Palace nabbed a 2-0 home win over Cardiff City to go level with them on 13 points.