The sides have won two games each all season and are at risk of being cut adrift should they fall to defeat this weekend.
West Brom enter this relegation six-pointer on the back of a 5-0 thrashing at the hands of Manchester City in midweek, making it five home league losses in a row.
The Baggies have shipped at least three goals in each of those defeats and have failed to score in the last four of them.
Indeed, each of the last 21 Premier League goals scored at The Hawthorns has been scored by the opposition - the longest run of goals at a stadium scored against a single team in the competition's history.
Sam Allardyce's men, whose only win in their last 10 outings overall in the league came against Wolverhampton Wanderers two weeks ago, are now seven points adrift of 17th-placed Brighton & Hove Albion.
Fulham are in a slightly better position, two points closer to Brighton and with a game in hand still to play, though no team is on a longer winless run in the division (nine matches).
However, the Cottagers look a stronger side now than they did in the first few months of the season, losing just two of their last eight league matches.
Too many games are being drawn, though, with Brighton the only team in the division to have drawn more times this campaign.
It came as little surprise, then, that those two teams played out a stalemate on Wednesday. Fulham were arguably second best at the Amex Stadium, though they could have snatched victory late on through chances for Aleksandar Mitrovic and Ruben Loftus-Cheek.
Three of the last four league meetings between West Brom and Fulham have also finished all square, meanwhile, with the Cottagers picking up the only victory in that sequence.
In fact, this is a fixture that the west London side tend to do well in, having gone eight without defeat against West Brom in the Premier League.
West Bromwich Albion Premier League form: DLLWLL
West Bromwich Albion form (all competitions): LLLWLL
Fulham Premier League form: DDDLLD
Fulham form (all competitions): WDLLLD
Allardyce will surely make changes on the back of the heavy loss to Man City, which could mean the ineffective Callum Robinson dropping out of the side.
At the opposite end of the pitch, Alphonse Areola is looking to keep successive Premier League clean sheets for the first time.
West Bromwich Albion possible starting lineup:
Johnstone; Furlong, Ajayi, Bartley, Gibbs; Gallagher, Sawyers; Snodgrass, Pereira, Phillips; Grant
Fulham possible starting lineup:
Areola; Aina, Andersen, Adarabioyo; Tete, Loftus-Cheek, Reed, Anguissa, Robinson; Cavaleiro, Lookman
We say: West Bromwich Albion 1-1 Fulham
It is still too early in the season to describe this as a make-or-break clash for either side, though both managers will see this as a huge opportunity to close the gap on safety.
West Brom have been abysmal on home soil since the start of December, while Fulham have looked good on their travels but are drawing too many games.
The Cottagers have drawn their last three away league matches, in fact, and we are backing this one to finish the same way - a result that will suit neither side.
Top betting tip
Watch the Sports Mole Football Shorts prediction for this game below: