The Reds dominated the opening period, although West Ham gave them a couple of minor scares, but looked like they would have to settle for 0-0 at the break until Guy Demel put through his own net three minutes from the interval.
It was two shortly after the break as Steven Gerrard's free-kick was put back across goal by Mamadou Sakho before being diverted into the net by James Collins.
Liverpool looked rampant but were pegged back shortly after the hour as another own goal, this time from Martin Skrtel got West Ham back into the game.
There was a nervy few minutes for the home side as the Hammers threatened an equaliser before a lovely move ended with Luis Suarez heading past Jussi Jaaskelainen.
The visitors were reduced to 10 men when Kevin Nolan went through the back of Jordan Henderson shortly afterwards before Joey O'Brien added to the own goal count as he inadvertently deflected Suarez's shot beyond Jaaskelainen.
The only downside to the day was the sight of Steven Gerrard limping off injured midway through the second half, which prompted a period of uncertainty which was in danger of developing into a terminal decline until Suarez's intervention.
In the first half, even with Philippe Coutinho pulling the strings and dropping deep from his position behind the main striker, West Ham appeared to have worked out a way to stifle Liverpool's primary threat.
Having seen a left-footed chip drift wide the 26-year-old was a lively presence in and around the penalty area and had a shot from Gerrard's pass deflected wide before getting in the way of Henderson's effort after he cut inside.
Raheem Sterling's pace on the diagonal run from the right started to open up the Hammers' defence - especially with Coutinho's weight of pass timed to perfection - but he lacked an end product and his scuffed shot having outpaced his opponents failed to trouble Jaaskelainen.
That task fell to Suarez, of course, whose angled shot just before the break was not held by the Finn and bounced into the path of Demel who diverted the ball back past his own goalkeeper.
It was just the lucky break the home side needed after a first half of toil.
West Ham could feel slightly aggrieved as they had created the best chance when Modibo Maiga's header was brilliantly tipped over by Simon Mignolet.
They also saw Matt Jarvis' cross evade Mignolet and roll through the six-yard area after Johnson had given away possession to George McCartney.
The goal forced the visitors to be more open after the break but only two minutes in they were further behind.
James Tomkins went through the back of Suarez and Gerrard's free-kick picked out Sakho at the far post.
The France defender, making his first start since the November 2 defeat at Arsenal, completely fluffed his shot but did just enough to divert it goalwards and Collins could not keep it from crossing the line.
But soon after Liverpool lost Gerrard to injury as he raced down the inside-right channel.
West Ham drew confidence from a sharp reflex save by Jaaskelainen to deny Sterling's first-time effort and then were handed a way back into the game when Skrtel scored his second own goal in a week after turning Jarvis' header past Mignolet.
That really cranked up the tension as the home side conceded the initiative and it was only wrested back thanks to Suarez.
Glen Johnson produced the perfect cross for the striker to head home at the far post and then smashed what would have been a second against O'Brien, across goal then home via the crossbar.
Uncharacteristically he squandered the chance of scoring another late goal after rounding Jaaskelainen with five minutes to go, instead running the ball out of play.