Oliver Glasner’s side took the lead in the semi-final through Eze’s long-range blast before Sarr netted twice in the second half.
In the final on May 17, Palace will face Nottingham Forest or Manchester City, who meet in the second semi-final on Sunday.
The Eagles have never won the FA Cup, losing their two final appearances against Manchester United in 2016 and 1990.
Villa, who last won the FA Cup in 1957, were hoping to make the final for the first time since 2015.
But Unai Emery’s team produced a dismal display and will have to settle for fighting to qualify for the Champions League via a top-five finish in the Premier League.
Jean-Philippe Mateta had the ball in the back of the net just before the half-hour mark, but it was chalked off after a VAR check confirmed the French striker had fouled Ezri Konsa in the build-up.
There was no such doubt about Eze’s opener, however, after Sarr got in the way of Pau Torres’ pass, then collected the resulting ricochet to the right of the Villa area.
Sarr found Eze and the midfielder curled a superb strike beyond the reach of Villa goalkeeper Emiliano Martinez.
Torres looked for an instant reply when he nodded just over the crossbar.
Konsa came closer, forcing Dean Henderson into a low save with a header of his own from a corner.
Villa piled on more pressure after the restart when Henderson made another fine save to deny John McGinn’s sharp volley, then Lucas Digne fired narrowly wide through a crowd of players.
Palace were awarded a 53rd-minute penalty after Eze was tugged down by Boubacar Kamara, and Mateta stepped up to the spot after a VAR check, but his shot clipped the post and went wide.
Just as Villa started to gain momentum, Adam Wharton intercepted a pass and, after a quick touch from Mateta, Sarr fired into the bottom corner.
Henderson repelled a blast from Villa substitute Leon Bailey, moments after Mateta slid in to deny Ross Barkley.
Sarr nodded Eze’s cross off target, while Matty Cash’s attempt to claw a late goal back for Villa sailed wide.
Sarr put the seal on Palace’s impressive performance in stoppage-time, outpacing Konsa before slotting home to send the Eagles into the final. (AFP)
