They missed the chance to move back up to fourth, and it leaves Arsenal in pole position in the race for the final Champions League spot.
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Puncheon, Dann and Jerome scoring for Palace while Corks Damien Delaney played in the centre of defence.
Meanwhile
Manchester City manager Manuel Pellegrini says his side won't give up on winning the title.
Their title chances suffered a huge knock last night, after drawing 2-all at home to bottom of the table Sunderland.
It leaves them six points behind leaders Liverpool, though they do have a game in hand.
Pellegrini says the result wasn't good enough.