The Toffees have lost four of their last six Premier League matches, while Palace's win over Norwich City last weekend ended a run of 14 league games without a victory. Both teams will be hoping to regain form ahead of their respective FA Cup semi-finals later this month.
Only one of the last 10 meetings between Crystal Palace and the Blues across all competitions has ended as a home win, but Palace have a good recent record against the Blues. The Eagles have lost just one of their last five Premier League matches against the Blues, winning twice and drawing on a couple of occasions.
There was nothing to separate the two sides when they last met in December. Scott Dann's header was cancelled out by Romelu Lukaku, who has scored in three consecutive appearances against Palace.
A crucial period for Everton and Martinez
Roberto Martinez has said he does not feel under added pressure despite growing criticism and the team's regression in the Premier League. The Toffees are 14th in the table following a run of three wins in 13 league games and the Everton supporters made their feelings clear during their side's 1-1 draw at Watford on Saturday.
Supporters displayed banners around Vicarage Road, which were visible evidence that all is not well on the blue half of Merseyside. "Martinez out" read one banner, while another said "Baines is one of us", referring to Martinez's reaction to the left-back's comments following the Manchester United defeat.
While the result against Watford ended a three-match league losing run for Everton, it did little to improve optimism among supporters. But, in a season with few positives for the Blues, their away record is certainly one. The Toffees have lost just two away matches this season, the joint-fewest in the Premier League along with Leicester City and Tottenham Hotspur.
There is no doubting that this is now a crucial period for Everton and Roberto Martinez. Supporters are visibly voicing their frustration with their side's form, players are expressing their concerns over the side's chemistry, but still Martinez remains positive stating he does not feel under added pressure. And with five games still to come this month, including a huge FA Cup semi-final against either Manchester United or West Ham United, this is definitely the biggest period in Martinez's Everton career.
The last time these two sides met, on 7 December, Crystal Palace were in sixth place and the talk at Selhurst Park was a possible European challenge, but just three league victories have followed and has seen Alan Pardew's side slide down the Premier League table.
A 1-0 win over Norwich City on Saturday ended a 14-match winless streak in the league starting before Boxing Day and the three points gained from beating the Canaries provided the Eagles with some breathing space from the drop, opening a 10-point advantage over Sunderland.
Palace have a number of quality players in their squad shown through their league position just a few months ago. Yohan Cabaye and Yannick Bolasie are both players to watch; while the signing of Emmanuel Adebayor in January has significantly boosted their striking options. With Everton's frailties in defence, keep an eye out for Scott Dann at set-pieces as he has already scored five goals this season, including in the reverse fixture.
Phil Jagielka will miss at least the next two games with the hamstring injury he sustained at Watford. The Everton captain limped off towards the end of the 1-1 draw at Vicarage Road and it has been confirmed he will miss this week's games at Crystal Palace and Southampton.
Tom Cleverley is battling to be fit enough to face Palace, while Ross Barkley is expected to be fine for the trip to Selhurst Park after recovering from a knock from Saturday's game.
Crystal Palace forward Emmanuel Adebayor has returned to fitness and is in the squad to face Everton, while James McArthur is back in training but the midfielder will not be considered for this match.