It has not all been plain sailing for Carlo Ancelotti since his arrival at the club, but there is no question that the Italian would have been delighted by his team's response at Watford last weekend after falling 2-0 behind.
The Toffees turned the game around to record a 3-2 win at Vicarage Road, meaning that they are unbeaten in the Premier League since a narrow 2-1 defeat at Manchester City on New Year's Day.
After this weekend, Everton will not play again until February 23 when they visit Arsenal, and a win in Saturday's early kickoff would actually move them into seventh position in the Premier League table.
Not since November 23 have the Merseyside giants lost a league match at Goodison Park, winning three of their last five in front of their own fans, who will be expecting another positive result on Saturday.
Everton have actually not lost to Palace in the Premier League since September 2014, although the last two league meetings between the two sides have finished in goalless draws.
Roy Hodgson deserves immense credit for the job that he continues to perform at Palace, but the experienced manager will certainly be concerned by his team's form in recent weeks.
Indeed, without a Premier League victory since Boxing Day, the Eagles have dropped into 14th position in the table. They are only actually six points clear of the relegation zone, suggesting that the club are far from safe despite impressing in the opening months of the campaign.
The capital outfit have lost their last two in the league to Southampton and Sheffield United without scoring, but they did pick up a point at Manchester City in their last away match on January 18.
Palace have actually only lost one of their last nine Premier League matches on the road, demonstrating that they are a much tougher proposition on their travels than at Selhurst Park.
The Eagles have been beaten on each of their last two visits to Goodison Park in the top flight, though, and will be the underdogs entering this weekend's clash on Merseyside.
Everton Premier League form: WLWDDW
Everton form (all competitions): LLWDDW
Crystal Palace Premier League form: DDDDLL
Crystal Palace form (all competitions): DLDDLL
Everton will again be without the services of long-term absentees Jean-Philippe Gbamin and Andre Gomes, while fellow midfielder Fabian Delph is suspended following his red card against Watford last weekend.
Ancelotti has no other concerns heading into the contest, though, and there are not expected to be too many changes to the side that started against Watford.
As for Palace, on-loan striker Cenk Tosun, who is carrying a hamstring issue, will be unavailable to face his parent club, but Hodgson's squad is looking a lot healthier following a series of issues in recent weeks.
Everton possible starting lineup:
Pickford; Sidibe, Mina, Holgate, Digne; Iwobi, Schneiderlin, Sigurdsson, Walcott; Calvert-Lewin, Richarlison
Crystal Palace possible starting lineup:
Guaita; Ward, Tomkins, Cahill, Van Aanholt; Ayew, Kouyate, Milivojevic, McArthur, Zaha; Benteke
We say: Everton 2-1 Crystal Palace
Palace have struggled for results in 2020 but certainly deserve respect for their away form. Everton will be feeling pretty good about themselves at the moment, though, and we fancy a narrow home win here.