The leaders broke the deadlock through Sadio Mane midway through the first half, but it was an unconvincing performance from Jurgen Klopp's side and the Hammers were well worth the point given to them by Michail Antonio's quickfire equaliser.
Indeed, the hosts may feel that they could have come away with all three points given that Liverpool's goal should have been ruled out for a clear offside in the buildup, and in the end it was the visitors who survived a string of clear chances to escape with a second draw in the space of a week.
The result does mean that Liverpool extend their advantage at the top to three points, but Manchester City will now have the chance to leapfrog them in the table by beating Everton on Wednesday night.
Liverpool had seen both Tottenham Hotspur and Man City close the gap with wins over the weekend, but the leaders were sluggish from the off and could have fallen behind within three minutes when Javier Hernandez curled narrowly wide after being teed up by Mark Noble.
Aaron Cresswell also came close in the opening 10 minutes as West Ham made the brighter start, with the full-back flashing a low drive just past the far post after some uncertain defending from the visitors.
Alisson Becker was then forced into his first save of the contest after 16 minutes when Hernandez was allowed the space to let fly from 25 yards, with the Liverpool keeper at full stretch to push the ball away.
The visitors finally responded with their first chance after 20 minutes when Roberto Firmino tested Lukasz Fabianski, although the Brazilian should perhaps have done better having broken into the box only to scuff his finish.
It proved to be a warning shot for West Ham, and Liverpool broke the deadlock against the run of play moments later when Mane turned smartly inside the area before picking out the bottom corner for his third goal in as many games.
Replays showed that the goal should not have stood, though, as the referee's assistant somehow failed to flag a clearly-offside James Milner before the Liverpool man provided the assist.
West Ham did not let any sense of injustice linger, though, and they restored parity just six minutes later when Liverpool were caught napping from a slick free kick routine which allowed Antonio to escape Naby Keita and pick out the bottom far corner from inside the area.
The hosts' set-piece routines caused Liverpool's uncharacteristically shaky defence problems throughout the first half, and Declan Rice should have given West Ham the lead four minutes before the interval when he was left completely unmarked inside the area only to put his header narrowly off target.
Liverpool would have been happy to reach half time level, although they almost produced a smash-and-grab second shortly before the interval when Mane got across his man and glanced Milner's free kick into the arms of Fabianski.
West Ham had looked the more likely to score for the vast majority of the opening 45 minutes, though, and they threatened again in the early stages of the second half when Issa Diop climbed highest from a corner to flick a header wide.
Liverpool continued to struggle to find any rhythm in the second half, although Mohamed Salah did begin to see more of the ball after a quiet first half and he fired a powerful strike into the arms of Fabianski six minutes after the restart.
The visitors were crying out for a moment of magic from their talisman, and he almost provided it shortly after the hour mark when he danced his way into shooting space inside the box only to put his curling finish too close to the keeper.
West Ham became more concerned with preserving their point than pushing for a winner as the second half wore on, but there were still moments of concern for Liverpool, and Noble came within inches of giving his side the lead 17 minutes from time after Felipe Anderson had bundled his way into the box.
It was one of a number of scares Liverpool survived over the course of the evening, but they almost snatched an undeserved late winner with the final action of the match when Keita squeezed a pass through for Divock Origi, whose shot lacked the power to beat Fabianski.
Once again the flag should have been raised but wasn't, although this time it did not prove to be a costly error from the officials and West Ham were content with a draw that ends their three-match losing streak across all competitions.
Liverpool, meanwhile, have now won just two of their six games in 2019 and could find themselves in second place by the time they return to action against Bournemouth on Saturday.
WEST HAM (4-2-3-1): Fabianski; Fredericks, Ogbonna, Diop, Cresswell; Rice, Noble (Obiang 79'); Antonio, Snodgrass, Anderson (Masuaku 91'); Hernandez (Carroll 79')
LIVERPOOL (4-3-3): Alisson; Milner, Matip, Van Dijk, Robertson; Lallana (Shaqiri 69'), Fabinho, Keita; Salah, Firmino (Origi 75'), Manebody check tags ::