Frank Lampard's Everton headed to Selhurst Park on the back of a morale-boosting and much-needed league win over Newcastle United yet despite a bright start they crashed out of the cup.
Palace's 3-1 win over Everton in December in the Premier League was its first against the Toffees in 14 matches and it was well on its way to another thanks to first-half goals from Marc Guehi and Jean-Philippe Mateta.
Patrick Vieira's team were hardly troubled after the break, and it capped off progression in style thanks to late goals from Wilfried Zaha and Will Hughes.
Everton might have been ahead inside the opening minute, but Ben Godfrey just failed to meet Michael Keane's scuffed shot.
Guehi survived a penalty claim after his sloppiness allowed Richarlison to pounce, though Everton's bright start was punctured when former Palace winger Andros Townsend suffered an apparent knee injury.
Palace made that break count, with the unmarked Guehi heading in from Olise's inswinging corner.
Zaha missed a great chance teed up by Mateta, yet the latter made no mistake when Palace's talisman returned the favour, drilling home first-time from a brilliant cutback, and only a last-ditch Seamus Coleman tackle prevented the striker doubling his tally before the break.
Dominic Calvert-Lewin was introduced at half-time, yet he had managed just eight touches by the time Demarai Gray went close in the 66th minute.
There was precious little quality to the visitors' play despite their precarious position and their FA Cup exit was confirmed in fittingly humbling fashion as a sliced Olise strike hit the post and fell for Zaha to nudge home.
Hughes similarly tapped into an empty net for Palace's fourth to the delight of a jubilant home crowd.