Notwithstanding that, even if the Hammers were to triumph over the Yorkshiremen, they would still need Everton to do them a huge favour by winning away at Tottenham; another tall order given that the Toffees had only won once in their last 16 games in the blue and white half of North London.
Leeds in better form
With four wins and two draws in their last six matches of the current campaign, the all whites were in much better form than an Irons squad who had won two, drawn one and lost three of their last six games.
Much was going to be expected of Jarrod Bowen, despite his disappointment at not being called up by Thomas Tuchel for the World Cup, though it was incumbent on every West Ham player to give absolutely everything on the day and hope it would be enough.
With the London Stadium bathed in sunshine, the Hammers faithful were in full voice, though they might've gone behind in the opening two minutes after a simple ball split the hosts' defence wide open, and only a clumsy challenge from Tomas Soucek snuffed out the chance.
The visitors made a better start, with Lukas Nmencha not able to sort his feet out when well placed, and a nervy beginning to the game from West Ham left them already chasing shadows by the 10-minute mark.
Summerville lively as West Ham grow into game
Crysencio Summerville remained lively against his old employers, with two early entries into the final third, and a 100% completion of his passes.
A sustained period of attacking play from the Irons almost resulted in the opening goal, with Pablo's on-target effort headed just over by Soucek.
Taty Castellanos' 100% one-on-one duel success in the opening exchanges and a 50% win rate from Mateus Fernandes, helped the Hammers to ease onto the front foot as the half continued.
El Hadji Malick Diouf also remained a combative presence down the hosts' left-hand side, winning possession back on three occasions before 20 minutes were on the clock.
Despite an evident urgency in West Ham's play, they still hadn't worked Leeds goalkeeper Karl Darlow until he parried a long-range effort from Fernandes wide, and only James Justin from the visitors' back four had needed to make a tackle.
Either a lack of composure when in possession, typified by Diouf's pathetic cross straight into Darlow's arms, or allowing Leeds to get back in numbers, meant that many of the Hammers' attacking forays were easily dealt with.
A hush fell upon the stadium each time the Yorkshiremen moved forward with any sort of purpose, but recently crowned Hammer of the Year, Dinos Mavropanos, stood tall every time, winning both of his aerial duels and two of his three ground one-on-ones.
The closest anyone would come to opening the scoring in the first half came 10 minutes before half-time, when Nmecha played in Dominic Calvert-Lewin, but the striker was thwarted by the quick reactions of West Ham's Mads Hermansen.
Tottenham goal silences the London Stadium
Aside from that save, the custodian did little else to give his defence any confidence, his 20% pass completion being by far the worst on show.
Mavropanos blocked another effort from Calvert-Lewin shortly afterwards, as Leeds began to take control of the game.
With Tottenham having taken the lead in their match, the atmosphere at the London Stadium became almost funereal in an instant.
What the West Ham game then needed was one of their players to put their head above the parapet and drag their teammates along with them.
Darlow was in the right place at the right time to smother Soucek's effort, whilst Pablo could only find the side netting from two yards out, and the boos that rang out at the half-time whistle spoke volumes.
Though the hosts had just shaded collective possession, it was Leeds who had made more total passes, were more accurate in their delivery, and had more passes in the attacking third of the field.
In essence, rather than grabbing the game by the scruff of the neck and going for the win, West Ham seemed fearful to lose, and that attitude appeared to stifle any creativity that might've helped the Irons out of the hole they were in as they headed to the dressing room.
Second-half improvement
Callum Wilson replaced Pablo at the break, and his impact could've been immediate as he fed Castellanos, but the latter made a complete mess of his chance.
The Argentinian then blazed high and wide when a pull-back to Wilson or Bowen would've been the easier option.
Despite needing that real battling performance from everyone, by the hour mark, all of Bowen, Soucek and Kyle Walker-Peters hadn't made a single tackle or interception.
That allowed the likes of Brenden Aaronson to push forward at will, and his four shots by that point were the most of any player on the pitch.
More urgency being shown by the visitors was a damning indictment of West Ham's players, who, despite having double the number of dribbles as their opponents (14 to seven), had won only half of those that Leeds had managed (42.9% to 85.7%).
Castellanos and Bowen's goals all for nothing
However, they were given a small amount of hope when Castellanos headed home from a corner with 25 minutes to play, and for a time at least, that completely changed the mood in the stadium, despite Tottenham still leading in their match.
Leeds remained calm, with Ethan Ampadu's magnificent 94.9% pass completion helping to take the sting out of West Ham's attempts to double their advantage.
That didn't stop Bowen rifling home a second, though the muted celebrations from players and supporters felt like there was an acceptance that it still wasn't going to be enough to keep the Hammers from falling into the Championship.
To West Ham's credit, they continued to press for another goal, and Wilson's brilliant late effort made it three, but the stands began to clear well before full-time.
Relegation was confirmed shortly after the final whistle, as news filtered through that Everton hadn't made the comeback which would've sent Spurs down in the Hammers' place.
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