Arsenal pressed for a winner in the nine additional minutes that remained, but Lerma and Benítez both made further crucial blocks, the latter another wonderful low save from close range to deny Declan Rice.
A draw was the least Palace deserved from the 90 minutes, even if for their second-half display alone.
But when the match went to penalties, for the third time this season for Palace, there awaited further cruelty for the Eagles.
Player after player stepped up and converted, both Arsenal and Palace scoring their first seven kicks of a high-quality shoot-out.
But after Saliba scored Arsenal’s eighth, Lacroix saw his low effort to Kepa’s right kept out, and Palace – by the narrowest of margins possible – eliminated at the Emirates for a second successive season at this stage.
Next up: a return to Premier League action, against Tottenham Hotspur at Selhurst Park, on 28th December.
Arsenal: Kepa (GK), Timber, Saliba, Calafiori, Lewis-Skelly, Norgaard, Merino, Eze (Odegaard, 67), Martinelli (Trossard, 59), Madueke (Saka, 67), Jesus (Rice, 85).
Subs: Raya (GK), Salmon, Zubimendi, Nwaneri, Gyokeres.
Palace: Benítez (GK), Canvot (Clyne, HT), Richards (Hughes, 75), Lacroix, Guéhi, Mitchell (Sosa, 90+11), Wharton, Lerma, Nketiah (Devenny, HT), Mateta, Pino (Uche, 85).
Subs: Henderson (GK), Rodney, Esse, Drakes-Thomas.
As It Happened