While the Toffees lost away against Newcastle United in midweek, the Eagles came from behind to beat Wolverhampton Wanderers on home soil.
Match preview
After steering Everton away from the relegation zone last season, Frank Lampard appeared to be building momentum with the Toffees at the start of this campaign, putting together a seven-game unbeaten run across all competitions between the end of August and the beginning of October.
However, the Merseysiders have since suffered three consecutive defeats, including the slender 1-0 loss away at Newcastle on Wednesday, and they have slipped to 15th in the Premier League table, just one point above the relegation zone.
Lampard has been left with plenty to ponder as they approach their final five games before the World Cup, but he will be hopeful that an encounter with Crystal Palace on Saturday can see them return to winning ways considering their recent record against the Eagles.
Everton are unbeaten in each of their last seven meetings against Palace at Goodison Park, including last season's 3-2 home victory in May which saw them come from two goals down to claim maximum points in dramatic fashion courtesy of an 85th-minute winner from Dominic Calvert-Lewin.
However, goals have been hard to come by on home soil so far this season as no top-flight team has scored fewer goals on their own turf than the Toffees, netting just three times in their first five league matches.
Everton registered just one shot against Newcastle, which failed to hit the target, so Lampard will be keen to see signs of improvement in the final third on Saturday.
Just over a week after coming from behind to beat Leeds United 2-1 on home soil, Crystal Palace replicated their success with another victory by the same scoreline at Selhurst Park against Wolves on Tuesday.
A 31st-minute header from Adama Traore broke the deadlock for the visitors before Eberechi Eze responded with a header of his own to restore parity two minutes after the break. Palace's star man Wilfried Zaha then completed the comeback with a composed strike in the 70th minute.
That result has seen Patrick Vieira's men climb into the top half of the Premier League, three points above Saturday's opponents Everton and six points behind the top five.
Indeed, closing in on the European positions before the World Cup begins cannot be ruled out for the Eagles, who are now preparing for four favourable-looking league fixtures against Everton, Southampton, West Ham United and Nottingham Forest.
However, three of these fixtures, including this weekend's trip to Goodison Park, are away from home and they are yet to get off the mark on their travels so far this term, drawing three times including two successive goalless stalemates - only Fulham back in December 2008 have ever played out three consecutive 0-0 draws in Premier League history.
Crystal Palace have also won only one of their last 15 top-flight meetings with Everton, a 3-1 victory at Selhurst Park last season, so they will need to be on top of their game if they wish to claim maximum points on Saturday.
Everton Premier League form:
D
W
W
L
L
L
Crystal Palace Premier League form:
D
D
L
W
D
W
Team News
Everton quartet Yerry Mina (calf), Andros Townsend (ACL), Ben Godfrey (fractured fibula) and Nathan Patterson (ankle) all remain sidelined with injuries, although the latter is hoping to return next month.
Calvert-Lewin was handed his first start of the season against Newcastle, lasting for 73 minutes, and the 25-year-old striker could retain his place in the first XI ahead of Neal Maupay.
With Idrissa Gueye's form dipping in recent weeks, either James Garner or Tom Davies could be handed a start in centre-midfield alongside Amadou Onana and Alex Iwobi - the latter of whom scored in Everton's most recent home game against Manchester United.
As for Crystal Palace, they are still without Nathaniel Clyne, Nathan Ferguson (both ankle), James McArthur (groin), Chris Richards (thigh) and Jack Butland (wrist) due to injury, while Will Hughes is doubtful with illness and will be assessed ahead of kickoff.
Vieira could be tempted to name the same starting lineup that beat Wolves in midweek, with Michael Olise continuing ahead of Jordan Ayew in the front three alongside Zaha and Odsonne Edouard.
Goalkeeper Vicente Guaita, who has kept two clean sheets and made 11 saves in his last two away games, is set to be protected again by a back four of Joel Ward, Marc Guehi, Joachim Andersen and Tyrick Mitchell.
Everton possible starting lineup:
Pickford; Coleman, Coady, Tarkowski, Mykolenko; Iwobi, Garner, Onana; Gray, Calvert-Lewin, Gordon
Crystal Palace possible starting lineup:
Guaita; Ward, Andersen, Guehi, Mitchell; Eze, Doucoure, Schlupp; Olise, Edouard, Zaha
We say: Everton 1-1 Crystal Palace
Both sides head into Saturday's contest off the back of contrasting results, with Crystal Palace looking to build on their midweek win and maintain their position in the top half of the table.