Plymouth secured back-to-back Championship wins thanks to striker Paul Gallagher's classy double.
The on-loan Blackburn man fooled Palace goalkeeper Julian Speroni with a clever curling shot in the 28th minute.
Gallagher sealed the spoils after collecting a high ball, cutting inside and shooting home low from 25 yards.
Palace striker Alan Lee made his full debut but was taken off at half-time and defender Paddy McCarthy headed home late on.
Crystal Palace boss Neil Warnock: "It's disappointing but now we have to muck on. It's a difficult time for us at the moment with players out, but that's life.
"I still felt at 1-0 we could win it but we'd already given one goal away from a corner and then conceded another from a long punt from their keeper. If Matt Lawrence had been any deeper he'd have had gloves on.
"Defensively we've been good at home but today both goals disappointed me and the lads know how I feel."
Plymouth manager Paul Sturrock: "Gallagher has found a niche in the hole and causes a lot of concern to other teams.
"If he carries on playing like that it won't be long before someone comes and has a peek at him. He's got a change of pace which is a bit special and he has great vision and is two-footed.
"He's got natural talent, but there have been a few changes of manager at Blackburn and for a young player like that it's difficult to fit in in the Premier League. So he's been from pillar to post but now he's starting to learn his trade and understand his game."
Crystal Palace: Speroni, Butterfield, Lawrence, Fonte, Hill, Ifill, Watson, Carle (McCarthy 66), Derry, Djilali (Griffit 72), Lee (Moses 46). Subs Not Used: Fletcher, Oster.
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