Roberto Martinez's men leapfrogged Arsenal with a scrappy 1-0 Premier League win at Sunderland on Saturday and now face the task of keeping the North London club at bay for the remainder of the season.
Regardless of Arsenal's result against West Ham on Tuesday, three points would be enough for Everton to remain in the driving seat in the race for fourth spot for the time being.
Ultimate success in their quest would see Everton competing in the UEFA Champions League for the first time since the 2005-06 season and, on paper, Palace at home would appear a reasonably straightforward stepping stone on the way to achieving that aim.
However, Tony Pulis' once relegation-threatened outfit have won their last three Premier League matches, beating Chelsea, Cardiff City and Aston Villa, and could yet finish in the top half - an unthinkable feat when the Welshman assumed the reins in December.
That record will give Palace hope, and Martinez knows the importance of making the most of his side's three remaining home fixtures.
"We've got three games at home and at Goodison (Park) our form has been very good but we're going to be heavily tested," he told Sky Sports.
"You look at it on paper and Arsenal have got the best run-in, but the good thing about football is nothing works as it should be on paper.
"We're excited that at this stage of the season we've got enough points to fight for that position and will try to take advantage of our home fixtures - that could be the difference of achieving it or not."
Thoughts of the drop have faded fast for Palace fans in recent weeks, but Pulis will be keen not to show Everton the hospitality his players received when this fixture was initially called off due to stormy weather at Goodison Park back in February.
Speaking at the time, Pulis said: "When the game was called off, they fed the players, they found us a hotel to stay in, they got us training facilities the next day and they paid for everything. They actually paid for everything.
"I just hope the chairman's already paid back what we owe them."
Palace should expect no such charity from an Everton side hungry for European football this time around.
Phil Jagielka (hamstring) is nearing a return for the hosts, but may not be quite ready in time for Wednesday's match, and trio Steven Pienaar, Darron Gibson and Arouna Kone (all knee), defender Bryan Oviedo (broken leg) and loanee Lacina Troare (hamstring) will miss.
Palace have a near fully fit squad, although Kagisho Dikgacoi was withdrawn early on at the weekend.
