Brendan Rodgers' side had plenty of possession but struggled to break down a resilient Hammers team that actually came closest to scoring when Jack Collison saw a header cleared off the line.
The result means the Reds remain in seventh, while Sam Allardyce's side edge closer to the safety of mid-table in their first season back in the Premier League.
Philippe Coutinho had spoken in the build-up to the game of his growing understanding with Luis Suarez and the little Brazilian was at the heart of Liverpool's best work before the break.
Although the home side dominated possession, chances were few and far between and it was West Ham with the best opening of the first half - created and spurned by Mohamed Diame.
The midfielder wriggled clear of two men in the corner then evaded a third before dancing past Steven Gerrard and Stewart Downing only to blaze over from close range.
Downing was substituted shortly afterwards with an injury and was replaced by Daniel Sturridge with the former Chelsea man adding more impetus to the Liverpool attack.
But despite plenty of pressure, with Suarez forcing a good save from Jussi Jaaskelainen down low, the Reds found the Hammers in resilient mood and the visitors got to the break all-square.
Liverpool upped the tempo after the interval with Gerrard to the fore as he saw a cross well cleared by Guy Demel before having a shot blocked on the line after clever play by Suarez.
The Reds skipper then thought he'd won a penalty in front of the Kop but, despite loud protestations, it was shown that James Tomkins got a slight touch on the ball after sliding in.
West Ham remained an intermittent threat on the break and nearly stole the points when Collison beat Pepe Reina with a header from a left-wing corner that Lucas somehow cleared off the line.
Liverpool huffed and puffed but they could find no way past a spirited West Ham defence led by the combative James Collins and the away side held on for a deserved point.