The 19-year-old Norwegian's first Premier League strike prevented the Bluebirds from falling six points adrift of the Baggies and top-flight safety.
The Welsh outfit could move level on points with 17th-placed Albion and drag Palace, who are five points ahead of them, right back into the relegation scrap with victory at the Cardiff City Stadium.
A shock 1-0 triumph over title-chasing Chelsea at Selhurst Park in their last outing boosted Palace's hopes of securing consecutive seasons in the Premier League for the first time.
It was their fourth home win in six matches, but their away form is not so encouraging, with the Eagles having not collected maximum points on the road since a Boxing Day success over Aston Villa.
Palace are hoping that the Moroccan striker could be fit to return following a month out with a hamstring injury and if he is, he could replace former Cardiff forward Cameron Jerome up front.
Thomas Ince, who rejected the chance to join Cardiff last summer, may again have to settle for a place on the bench alongside fellow January arrival Wayne Hennessey, who has yet to play for the Londoners.
The midfielder, who had previously not scored for the Welsh outfit, now has seven for the season in only 20 starts, while defender Steven Caulker has also proved a valuable source of goals with five.
It is defensively where Cardiff have slipped up under Solskjaer, and conceding twice in the opening 10 minutes against Albion forced the former Manchester United star into a tactical rethink.
Fabio da Silva was hauled off in the first half and replaced by Old Trafford loanee Wifried Zaha as the Bluebirds switched to a 4-4-2 system, which they may employ from the start against Palace.
Eagles chairman Steve Parish has admitted his interest in resigning Zaha this week, but the ex-Selhurst Park favourite could line up against the team that he inspired to promotion on Saturday.
Possible starting lineups
Cardiff: Marshall, Theophile-Catherine, Turner, Caulker, Taylor; Zaha, Medel, Gunnarsson, Mutch; Daehli, Campbell
Palace: Speroni; Mariappa, Dann, Delaney, Ward; Dikgacoi, Jedinak, Ledley; Bolaise, Puncheon, Jerome
Sports Mole says: 2-1