Marco Silva's side most recently went down 2-1 to relegation-threatened Bournemouth, while the Hammers' demotion fears deepened with a 5-1 loss to Newcastle United on Wednesday.
Match preview
With Aleksandar Mitrovic beginning his lengthy suspension and the threat of sanctions on manager Marco Silva also looming, morale was not on Fulham's side for their trip to Bournemouth, and the Cherries needed no second invitation to take advantage of the Cottagers' predicament.
Andreas Pereira's 16th-minute strike broke the deadlock, but Marcus Tavernier's wonderful equaliser preceded Dominic Solanke's winner to prolong Fulham's misery on and off the field, as their European hopes continue to dwindle by the week.
Now enduring a miserable four-game losing run across all tournaments - including each of their last three in the top flight - this weekend's hosts have plummeted to 10th in the rankings and cannot rise any higher up the table no matter what transpires by the close of play this weekend.
The Cottagers also sit level on points with Chelsea - albeit with a game in hand on the Blues - and the fight for a top-seven finish is far from done and dusted, but recent defensive failures have done Fulham no favours whatsoever in their bid to crash the continental party.
Indeed, the Cottagers have conceded at least two goals per game in their four recent losses, and only one of their last four Premier League matches at Craven Cottage has ended in victory, but West Ham fans will no doubt make the trip across the capital in hope rather than expectation.
While admitting that his job is now in "jeopardy" as West Ham continue to dance with the devil, one had to feel a shred of sympathy for David Moyes, who could not have done anything to prevent two catastrophic individual errors during Newcastle's demolition job.
Lukasz Fabianski and Nayef Aguerd would have welcomed the London Stadium turf opening up and swallowing them whole on Wednesday, as Callum Wilson and Joelinton both hit braces alongside Alexander Isak's lob to render Kurt Zouma's header inconsequential.
The few West Ham souls that stayed until the bitter end made no bones about their side's dismal display, but Moyes seemingly retains the trust of the powers-that-be for now, as the Hammers remain embroiled in a nine-team relegation dogfight - sitting in 15th place as the highest of four teams on 27 points thanks to a superior goal difference.
Prior to the Newcastle-inflicted humiliation, West Ham had strung together a four-game unbeaten run - attention will soon turn to their Europa Conference League quarter-final with Gent after seeing off AEK Larnaca with ease - but Moyes's side have been nothing short of horrendous on the road; failing to win in 11 Premier League away games since edging past Aston Villa 1-0 in August.
Recent history does favour the Hammers, though, as Fulham have lost four and drawn one of their last five meetings with their capital counteparts - including a 3-1 reverse at the London Stadium in October - since Steve Sidwell and Dimitar Berbatov were among the goals in a 2014 New Year's Day win.
Fulham Premier League form:
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Fulham form (all competitions):
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West Ham United Premier League form:
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W
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D
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West Ham United form (all competitions):
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Team News
Fulham talisman Mitrovic was slapped with an eight-game ban for shoving referee Chris Kavanagh in their FA Cup loss to Manchester United - he served the first game of that suspension at the Vitality Stadium - while manager Silva will not be on the touchline this week as he begins a two-game ban.
Further punishment could be on the way for the pair, with the FA feeling that the sentences handed down were too lenient, but Willian is back from a suspension of his own and could threaten to demote Bobby De Cordova-Reid down to the bench.
Neeskens Kebano (Achilles) and Layvin Kurzawa (knee) represent the hosts' only two injury concerns at present, while centre-back Issa Diop will expect to line up against his former employers.
The West Ham treatment room is also relatively empty barring knee victim Gianluca Scamacca, whose first season in England has not gone at all to plan, and the Italian striker will undergo rehabilitation for at least the next two weeks.
Moyes should be tempted into a change up top anyway, as Danny Ings prepares to demote Michail Antonio back down to the bench, while Said Benrahma's position could also come under threat from Maxwel Cornet.
Neither Aguerd nor Fabianski should be at risk of losing their places despite their high-profile mistakes against Newcastle, but Vladimir Coufal is waiting in the wings to displace Thilo Kehrer as Moyes ponders changes across the field.
Fulham possible starting lineup:
Leno; Tete, Diop, Ream, Robinson; Palhinha, Reed; Willian, Pereira, Solomon; Vinicius
West Ham United possible starting lineup:
Fabianski; Coufal, Zouma, Aguerd, Emerson; Soucek, Rice; Bowen, Paqueta, Cornet; Ings
We say: Fulham 1-0 West Ham United
A spate of strong results against Fulham may give the Hammers faithful cause for optimism, while the absences of Silva and Mitrovic does not spell success for the leaky Cottagers either.