The Baggies ended their winless run with a 1-0 victory at fellow strugglers Sheffield United, but they remain inside the relegation zone heading into the weekend.
Palace have lost back-to-back matches to slip down to 15th, meanwhile, albeit still seven points above the dotted line.
Slaven Bilic described last week's victory over Sheffield United as a huge psychological boost for his players given the weight of pressure on their shoulders ahead of the game.
Albion had lost six and drawn three of their opening nine matches since returning to the Premier League before Conor Gallagher's strike got them off the mark with a first win.
With Fulham also winning last time out, the Baggies are still in the relegation zone, one point behind Scott Parker's side.
Bilic will now be hoping to pick up back-to-back wins for some much-needed momentum, knowing that his side have trips to Manchester City and Liverpool over the next three weeks.
Palace are equally in need of the points on the back of defeats to Burnley and Newcastle United without scoring.
In fact, the Eagles have lost three of their last four matches without finding the net, the exception in that run being a 4-1 victory at home to Leeds United.
It is proving to be a familiar story for Palace, who regularly blow hot and cold, never good enough to challenge for Europe but too good to be dragged into the bottom three.
It means that since keeping a clean sheet in their opening-weekend victory against Southampton, Palace have conceded in each of their last nine Premier League matches.
On the subject of goals, opponents West Brom's first four league games saw a total of 18 scored at an average of 4.5 per game, compared to seven in the last six (1.2 per game).
Palace are unbeaten in their last four games with Albion, winning three and keeping a clean sheet each time, but they have won only once in six top-flight visits to The Hawthorns.
West Bromwich Albion Premier League form: DDLLLW
Crystal Palace Premier League form: DWLWLL
Jake Livermore has missed West Brom's last two games after testing positive for coronavirus, but he is now officially back in contention after self-isolating for two weeks.
However, with Chelsea loanee Gallagher impressing with his winner against Sheff Utd, it may well be that Livermore has to settle for a place among the subs.
In terms of the visitors, star attacker Wilfried Zaha is expected to be given the all clear to play this weekend following a period of self-isolating.
Palace have the oldest average starting XI in the Premier League this season (29 years, 132 days), with their last game against Newcastle the oldest so far (30y 182d).
West Bromwich Albion possible starting lineup:
Johnstone; Ajayi, Ivanovic, Bartley; Furlong, Gallagher, Sawyers, Gibbs; Pereira; Robinson, Grant
Crystal Palace possible starting lineup:
Guaita; Clyne, Kouyate, Cahill, Van Aanholt; Townsend, Riedewald, McArthur, Eze; Ayew, Batshuayi
We say: West Bromwich Albion 0-0 Crystal Palace
Palace have lost back-to-back away games in the Premier League without scoring, while West Brom have lost only one of their last four at home, keeping a couple of clean sheets.
Albion could really do with a win ahead of some tough games, but this may well turn out to be a perfect example of two sides cancelling each other out.
Top betting tip
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