Despite a dominating performance from Liverpool, a fantastic West Ham defensive display secured a well-deserved goalless draw at Anfield.
The hosts bossed possession in the first half but were unable to find their way through West Ham's defensive line, allowing the visitors to hit them on the counterattack with Mohamed Diame's lofted shot arguably being the best chance of the first period.
Liverpool continued their dominance after the restart and despite a multitude of chances and Daniel Sturridge having a goal rightly ruled out for offside, West Ham held on to pick up a point.
Brendan Rodgers named an unchanged starting 11 from the one that defeated Aston Villa 2-1 last weekend, with both goalscorers Jordan Henderson and captain Steven Gerrard starting in the centre of the field.
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 win all three points, Liverpool started the stronger, dominating the bulk of possession with ease and putting pressure on the rigid West Ham defence.
However, the visitors' tactic of crowding out the Liverpool attack seemingly worked wonders, 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 forced the game to move up a gear, but despite exhibiting some clever attacking play and having two-thirds of possession, Liverpool were unable to fully breach the West Ham defence for the rest of the first half.
The second half started as the first ended, and both Suarez and Gerrard were on hand to fire in early chances and put even more pressure on a West Ham defence that were looking as if they were moments away from reaching breaking point.
They continued to hold firm, however, and Tomkins especially was the most important rock in the rigorous 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 Henderson's low shot on goal hit Sturridge and flew past Jussi Jaaskalainen into the back of the net, but Sturridge was rightly flagged for offside and the Hammers were able to breathe a sigh of relief.
The onslaught continued and chances rained down in abundance on West Ham's Finnish shot-stopper, 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.
The referee pointed straight away for a corner, however, and the visibly tired visitors regrouped and regained their composure.
With 10 minutes left on the clock, Liverpool threw every available body forward in an attempt to snatch a last-minute winning goal, 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