Sam Allardyce’s rescue mission reached crisis point after goals from Declan Rice, Jarrod Bowen and Manuel Lanzini denied them the victory their new manager admitted they needed to have any realistic chance of staying up.
Allardyce arrived at Elland Road as a last-ditch appointment with four games to go, but his first three matches have provided just two points.
Moreover, should Leicester beat Newcastle on Monday night, the Whites will start the final day second from bottom.
They got off to a great start at the London Stadium as well, with Rodrigo volleying them into an early lead.
But Rice, named West Ham’s player of the year before kick-off – six years to the day since he made his debut against Burnley – marked what is likely to be his last home game for the club by equalising with his 15th goal in claret and blue.
The Hammers, safe from relegation and with a Europa Conference League final to look forward, should have been easy pickings. They even walked out carrying their children as mascots, giving a distinct end-of-season feel to proceedings.
But Bowen’s 12th goal of the season and a late strike from Lanzini saw them sign off from the London Stadium with only their second win in six matches to leave Leeds in deep, deep trouble.
Yet Leeds took a deserved lead after 17 minutes, albeit thanks to some awful defending.
West Ham had conceded to a long throw at Brentford last weekend but clearly had not learned their lesson. Fiorentina, their European opponents in Prague next month, should take note.
This time they somehow let a throw from Weston McKennie float on to the left boot of Rodrigo, who swept it first time into the net from 10 yards out.
However, Leeds lost Patrick Bamford to injury moments later, and with him went much of their attacking spark.
The Hammers may have been off the pace, but they equalised in the 32nd minute with a delightful goal from Rice.
Pablo Fornals, the goalscoring hero at AZ Alkmaar on Thursday night, scooped the ball over the Leeds defence to Bowen, whose chip across goal was sidefooted into the ground and up into the roof of the net by the England midfielder, who has been heavily linked with a big-money summer move.
Leeds should have gone back in front before half-time when Rodrigo robbed Kurt Zouma and cut the ball back but Wilfried Gnonto, on for Bamford, took an air-shot before Jack Harrison sliced his shot wide.
Allardyce’s response on the touchline, throwing his arms in the air in frustration, said it all.
They paid the price with 18 minutes left when Danny Ings played in Bowen, who slipped the ball past Robles.
Then substitute Lanzini, another likely to leave West Ham in the summer, tucked in Paqueta’s cut-back – despite a VAR check appearing to show the Brazilian was offside – to send Leeds spinning to what looks likely to be an extremely costly defeat.