The Eagles eventually added their third after Agbinone was once again fouled in the box, with the forward this time tucking the penalty in off the left post in 65th minute for his fifth goal in his last six matches.
Palace almost scored a fourth when Gibbard slipped past three defenders and fed Casey, on as a substitute, though his close-range shot was saved.
Reading substitute Verrell George forced Eastwood into only his second real save of the game in the 77th minute before Palace were reduced to 10 players when Walker-Smith picked up a second yellow card shortly after.
Trialist A came close for the Royals in stoppage time, letting fly from long distance with a strike that was saved by Eastwood, but the Eagles held on to keep a clean sheet and end the 2023/24 season on a high note.
Reading: Rhone (GK), Osho, Source (Irish, 81), Beacroft, Kanu (George, 45), Sackey, Trialist A, Howard, Barough, Trialist B, Timberlake (Duah, 45)
Subs not used: Sharlott (GK), Daka
Palace: Eastwood (GK), Grante, Walker-Smith, Browne, Cowin, Austin, King (S. Williams, 71), Gibbard (Adams-Collman, 71), Lusale, Trialist (Casey, 60), Agbinone (Lameiras, 71).
Sub not used: Hill (GK)