Said Benrahma struck a glorious equaliser to set up a grandstand finish, but they could not find the winner.
With the Hammers realistically needing to win their three remaining games to stand a chance of a Premier League top-four finish, the result leaves David Moyes’ side needing a miracle to beat Chelsea or Leicester City to Champions League qualification.
West Ham now sit five points points behind fourth-placed Chelsea with two games remaining, and will realistically need the Blues to lose both their remaining games.
The saving grace for Moyes is that Chelsea are in poor form having lost against Arsenal in midweek and then falling 1-0 in Saturday’s FA Cup Final against Leicester, and also face the Foxes in the League on Tuesday – so anything is possible.
But with West Ham held, that leaves Liverpool – currently fifth – as the likeliest challengers to Leicester and Chelsea’s top four hopes, with the champions four points behind Thomas Tuchel’s Blues with a game in hand.