The 10-man Toffees dug in for a goalless draw at Selhurst Park in the original contest, and either Luton Town or Bolton Wanderers will be awaiting the victors later this month.
Match preview
A trio of Toffees players looked on in utter bewilderment as Chris Kavanagh reviewed a challenge from Dominic Calvert-Lewin on Nathaniel Clyne during Everton and Palace's cup clash on January 4, where the striker went in high but seemingly avoided doing serious damage to his opponent.
Nevertheless, Kavanagh questionably saw fit to whip out the red card - which would be the headline story of that 0-0 affair in the English capital - but the Eagles failed to make the most of playing the final 15 minutes with an extra man on the pitch.
Everton have since succeeded with an appeal against Calvert-Lewin's sending off, which added yet more fuel to the fire over the perpetual VAR debate, but it was Sean Dyche's men who were on the correct end of a technological call during another goalless stalemate with Aston Villa in the weekend's Premier League battle.
Alex Moreno and Abdoulaye Doucoure both had strikes ruled out for offside on the Goodison turf - the former's took much longer to review, and while that point snapped Everton's three-game losing run in the Premier League, it is now no wins in six for Dyche and co.
Everton have seemingly fallen back into old attacking habits too, as the Toffees are now without a goal in three straight matches, but they have triumphed in each of their last four FA Cup replays at Goodison Park and have not been beaten in such circumstances since 1993-94.
While Everton exerted themselves for over 90 minutes at the weekend, Palace were one of several Premier League teams to enjoy the rare luxury of a free weekend, giving Roy Hodgson plenty of time to mull over his side's shortcomings from their initial stalemate with the Toffees.
Despite failing to get the job done against a 10-man Everton outfit, Palace's draw at least marked an improvement on their 3-2 loss to Dyche's men in November's Premier League battle, and the Eagles have regained a touch of resilience over the Christmas and New Year period.
Indeed, only one of Crystal Palace's last five matches across all tournaments has ended in defeat - and even then Chelsea only bested their London rivals 2-1 - and Hodgson's side boast praiseworthy points against Manchester City and Brighton & Hove Albion in that sequence, not to mention a morale-boosting beating of Brentford.
Confidence levels could plummet should Palace suffer a fourth FA Cup third-round exit in five seasons, though, and the Eagles' winless run on the road now stands at four matches, but their most recent FA Cup replay in the 2016-17 season ended in a 2-1 success over Bolton Wanderers in the third round.
History favours the men in blue, though, as they have prevailed in each of their previous two FA Cup replays with Palace - albeit in games that happened all the way back in 1907 and 1972 - and they have strung together an eight-match unbeaten run versus the Eagles at Goodison Park since an enthralling 3-2 loss in 2014.
Everton FA Cup form:
D
Everton form (all competitions):
L
L
L
L
D
D
Crystal Palace FA Cup form:
D
Crystal Palace form (all competitions):
L
D
D
L
W
D
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Team News
Despite being stretchered off the field with what was feared to be a serious ankle injury against Crystal Palace, Dwight McNeil was surprisingly fit enough to make the bench on Sunday and even came on for a 30-minute cameo against Aston Villa.
Calvert-Lewin is, of course, available after his punishment was rescinded, but Dele Alli (groin) ad Ashley Young (knock) will spend another couple of weeks in the medical bay, while Idrissa Gueye is on Africa Cup of Nations duty.
The fit-again McNeil ought to come into contention for a start given the rapid turnaround, which should also boost Beto and Andre Gomes's hopes of some valuable minutes. In between the sticks, meanwhile, Joao Virginia should replace Jordan Pickford.
With no Premier League commitments for Palace to factor in over the weekend, Hodgson will likely be working with the same group of players from their Selhurst Park stalemate, and the pairing of Rob Holding (ankle) and Sam Johnstone (calf) should not be too far away from returns.
However, there is still no official timeframe on Michael Olise's recovery from a hamstring problem - although he is expected to miss the rest of the month - while Cheick Doucoure (ankle), Joel Ward (thigh) and Jesurun Rak-Sakyi (thigh) are still absent too.
Jordan Ayew's departure for the Africa Cup of Nations also allowed Matheus Franca to make his maiden Palace start against Everton in the first encounter, but Hodgson conceded that the 19-year-old would not have been pleased with his 71-minute performance.
Everton possible starting lineup:
Virginia; Patterson, Tarkowski, Branthwaite, Mykolenko; Harrison, Onana, Garner, Gomes, McNeil; Calvert-Lewin
Crystal Palace possible starting lineup:
Henderson; Clyne, Andersen, Guehi, Mitchell; Lerma, Richards, Hughes; Eze, Mateta, Schlupp
We say: Everton 1-1 Crystal Palace (a.e.t, Everton to win on penalties)
A 13-day rest ought to have done Palace's shot-shy attackers the world of good, while jellied legs are sure to at least slightly hinder Wednesday's hosts, but their dogged display against a title-chasing Aston Villa is to be commended.