Jarrod Bowen put the home team ahead in the closing minutes of a forgettable first half but Andy Robertson levelled after the break.
A bizarre Alphonse Areola own goal 20 minutes into the second period put the visitors in front but Michail Antonio pulled West Ham level in the 77th minute.
The single point leaves Liverpool third in the table on 75 points, one behind defending champions Manchester City, who have two games in hand.
Leaders Arsenal are two points clear of Liverpool and have a game in hand.
Liverpool were on the front foot from the start at the London Stadium but energy quickly drained out of the encounter and the atmosphere went flat.
West Ham midfielder Lucas Paqueta was lucky to escape punishment after a reckless early tackle on Liverpool's Alexis Mac Allister.
The contest livened up in the closing minutes of the first period, with Luis Diaz hitting the post for the visitors in the 40th minute after good work down the left.
Two minutes later Liverpool goalkeeper Allison Becker was called into action, making a sharp save from Bowen's deflected shot.
But he was powerless to keep out Bowen's header from the resulting corner, which took the England forward to 16 Premier League goals this season.
Liverpool emerged for the second half with renewed intent and Ryan Gravenberch fired over from the edge of the box.
But they were back on terms in the 48th minute when Andy Robertson squeezed a shot past Areola at his near post.
Gravenberch attempted a flick minutes later but the chance went begging.
Angelo Ogbonna then made a crucial block as the game opened up before Trent Alexander-Arnold's shot from distance was saved.
But Liverpool got their noses in front in the 65th minute after Cody Gakpo's shot hit Ogbonna, Tomas Soucek and Areola on its way into the net.
The visitors had chances to pull further ahead but Antonio headed home a Bowen cross in the 77th minute to level.
Jurgen Klopp threw on Mohamed Salah, Darwin Nunez and Joe Gomez immediately after the goal in a desperate search for a winner.
Salah, who appeared to direct angry words at Klopp before he was introduced, raced forward as the clock ticked down.
His pass went behind Nunez but Harvey Elliott picked up the ball, rattling a shot off the crossbar.
Liverpool were on track for a trophy quadruple just weeks ago but Klopp's final season in charge is unravelling quickly after exits from the FA Cup and Europa League, accompanied by patchy Premier League form.
West Ham boss David Moyes, who last season delivered the club's first major trophy for 43 years, has been coy over his future but the club have an outside chance of qualifying for Europe.
