With just over 15 minutes remaining, second-half substitute Zack Henry notched his first goal of the campaign - giving Palace some breathing space and the vital second goal they needed to move to the top of the group.
The south Londoners saw off their northern counterparts in the time that remained, but it was Liverpool who qualified as group winners - winning 3-1 away at Birmingham City to go ahead of both Palace and Arsenal on goals scored.
Arsenal: Ranson (GK), Salmon, Ismail (Chapman, HT), Onyekachukwu, Sweet, Ibrahim, O’Neill (Oyetunde, 66), Copley, Zecevic-John (Murisa, 76), D. Casey, Bailey-Joseph.
Subs not used: Talbot (GK), Marciniak.
Palace: Hill (GK), King, Benamar, Adams-Collman, Somade, Muwana (Okoli, 64), Whyte, Danaher, Montjen (B. Casey, HT), Derry (Lameiras, 88), Osei (Henry, 60).
Subs not used: Mason (GK)