Despite a determined attacking performance by the hosts, a resolute display led by the Hammers' defence ensured that Sam Allardyce's team returned to east London with a point
The hosts bossed possession in the first-half but were unable to find their way past the Hammers' defensive line, allowing the visitors to hit them on the counterattack with Mohamed Diame's lofted shot arguably the best chance of the first period.
Liverpool's dominance continued after the restart and despite a multitude of chances - Daniel Sturridge saw a goal correctly ruled out for offside - West Ham held on to pick up a pleasing point.
Brendan Rodgers named an unchanged starting XI after victory over Aston Villa last weekend, with goalscorers Jordan Henderson and captain Steven Gerrard starting in the centre of midfield.
Meanwhile, Sam Allardyce made two chances to the side that beat West Brom 3-1 last Saturday, with, as expected, the ineligible Andy Carroll being replaced by Carlton Cole and James Tomkins coming in for the injured Winston Reid in the centre of defence.
Heavy favourites to collect all three points, Liverpool started the strongest of the two sides, dominating the bulk of possession with ease and putting considerable pressure on the rigid West Ham defence.
However, the visitors' tactic of crowding out the Liverpool attack proved effective, and they were able to carve out the first real chance on goal after 24 minutes when Diame beautifully weaved his way through the Liverpool defence and into the penalty area before letting himself down at the last minute with a lofted effort that cleared Pepe Reina's crossbar.
The Senegalese midfielder's strike took the game up a gear, but despite exhibiting some wonderful and clever attacking play and having two-thirds of possession, Liverpool were unable to fully breach the terrific West Ham defence for the rest of the first half.
The second half started as the first ended, with both Luis Suarez and Gerrard on the end of early chances, as the Reds piled the pressure on a West Ham defence that was looking as if it was moments away from reaching breaking point.
They continued to hold firm, however, and Tomkins in particular was a rock in the middle of Allardyce's back line, continuously throwing his body into last-ditch tackles and clearing a shot from Gerrard off the line to deny Liverpool an early second-half lead.
After over an hour of dealing with intense pressure, the West Ham defence was finally breached and Liverpool put the ball into the back of the net when Jordan Henderson's low shot on goal hit Sturridge and flew past Jussi Jaaskalainen into the back of the net. Sturridge, though, was rightly flagged for offside and the Hammers were able to breathe a sigh of relief.
The onslaught continued as chances rained down on West Ham's Finnish goalkeeper, and with 20 minutes left to play Liverpool had a penalty shout turned down when Gerrard appeared to be tripped over by the outstretched legs of Tomkins as he sprinted into the penalty area.
With 10 minutes left on the clock, Liverpool threw every available body forward in an attempt to snatch a last-minute winner, but, as was the case all afternoon, West Ham stayed composed at the back and hit Liverpool on the counterattack, forcing Lucas to save the hosts from losing the game in the dying moments when he cleared Jack Collison's headed effort off the line.