The pair are two of only five clubs to have won both of their opening games in 2020-21, and they come into this weekend's match after particularly encouraging results last time out.
Crystal Palace fans would have had every right to come into the new season with a feeling of trepidation; they ended 2019-20 in dreadful form and began the campaign with a difficult run of fixtures - hosting a Southampton side that boasted a brilliant away record last term before travelling to Old Trafford.
Six points from those two games is beyond what even the most ardent supporter would have expected, but last weekend's 3-1 win at Manchester United continued their perfect start to the campaign.
Wilfried Zaha was the star of the show against his former club as he scored in back-to-back league games for the first time since November 2019, and his apparent return to his best form helped Palace to register more than two goals for the first time in 40 top-flight outings.
A second-round EFL Cup exit on penalties to Bournemouth means that it has not quite been a faultless start overall, but Roy Hodgson's side will still go into this match against Everton full of confidence and knowing that victory would send them temporarily top of the table at this very early stage of the season.
The Toffees briefly sat at the summit following their 5-2 victory over West Bromwich Albion last weekend and, while they have since been nudged back down to second, it has still been a very encouraging start to the campaign for them as well.
James Rodriguez has fitted in immediately, Everton's other summer signings have also made bright starts and Dominic Calvert-Lewin leads the Premier League scoring charts following his hat-trick against the Baggies.
All in all, there is every reason for Carlo Ancelotti to be optimistic about the season ahead, with the Merseysiders having won their opening two league games for the first time since 2012-13, when they finished sixth.
It is not just in the Premier League that Everton are developing a winning habit, though; victories over Salford City and Fleetwood Town by three-goal margins - the latter of which saw Everton record a 5-2 triumph for the second time in four days - have seen the Toffees progress to the EFL Cup fourth round, where they will face West Ham United.
A couple of Jordan Pickford mistakes in that win over Fleetwood did raise concerns whether the England number one could be something of a liability in Everton's bid to finish in the top six, but Ancelotti was quick to brush off such accusations.
Pickford made two vital saves on Everton's last visit to Selhurst Park as the two sides played out a goalless draw on the opening day of the 2019-20 season, and early signs from Palace suggest that he could be busier still this time around.
However, Everton have not lost away to Palace in any competition since 1994 and are unbeaten in this fixture home or away in the last 11 editions.
Crystal Palace Premier League form: WW
Crystal Palace form (all competitions): WLW
Everton Premier League form: WW
Everton form (all competitions): WWWW
Both sides are still suffering from defensive shortages ahead of this match, although Palace's troubles could be slightly eased if Jairo Riedewald proves his fitness in time.
Former Liverpool striker Christian Benteke could be in contention as he works his way back towards full fitness, although Hodgson is unlikely to tinker too much with a winning formula, meaning that Michy Batshuayi could once again start among the subs.
Crystal Palace possible starting lineup:
Guaita; Ward, Kouyate, Dann, Mitchell; Townsend, McArthur, McCarthy, Schlupp; Zaha, Ayew
Everton possible starting lineup:
Pickford; Coleman, Mina, Keane, Digne; Doucoure, Allan, Gomes; Rodriguez, Calvert-Lewin, Richarlison
We say: Crystal Palace 1-2 Everton
This is a tricky contest to call; Everton lost 11 times away from home last season but look like a much better outfit this time around and have already ended their London hoodoo this term by winning at Tottenham Hotspur on the opening day.
It is a game both teams will fancy their chances of winning, but man for man Everton have the superior squad and so we are backing them to just about edge it and continue their perfect start.
Top betting tipOur expert tipster partners at Sporita.com are predicting over 1.5 goals in this match. Click here to find out what else they are predicting for this game and for more of their tried-and-tested football tips.Over 1.5:data
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