Veteran manager Hodgson, 73, announced on Tuesday he will be leaving the club at the end of the season after four years in the job and was given a heart-felt reception from the returning home supporters.
But his farewell match at Selhurst Park ended in a last-gasp defeat as Gabriel Martinelli latched onto fellow substitute Martin Odegaard’s cross to convert from close range on 91 minutes before Nicolas Pepe coolly rolled in Arsenal’s third four minutes later.
Christian Benteke’s diving header from Andros Townsend’s free-kick levelled for the home side after Pepe had volleyed in to finish off a neat Arsenal move.
Palace can move up a place to 12th on the final day if they better Wolves’ result against Manchester United, while Arsenal kept alive their hopes of a top-six finish.