Moses leads the celebrations as Palace win their third game of 2009
Swansea City suffered their second home defeat of the season as Crystal Palace dented their Championship play-off bid.
Victor Moses opened the scoring for the visitors after Swans sub Matty Collins had hit the post with a 20-yard shot.
Jose Fonte's close-range header doubled the lead after Anthony Stokes had flicked on Nick Carle's free-kick.
Gorka Pintado's 65th-minute goal gave Swansea hope of avoiding only a second loss in 20 games but Shefki Kuqi sealed Palace's win with an injury-time goal.
Swansea City manager Roberto Martinez said: "It wasn't the result that we were looking for and we are disappointed with certain aspects of our play as we played with our heart instead of our head.
"Crystal Palace were well organised but defensively we conceded very soft goals, one from a set-piece and the other we didn't deal with a long ball and that is disappointing.
"We were focusing on the result and not the performance and that shows anxiety. We were not at our best, accepted it and allowed Crystal Palace to take the three points.
"They had three shots on target and scored three times. The 3-1 defeat doesn't reflect the game but we have to learn from that."
Crystal Palace manager Neil Warnock said:
"I thought it was a team performance and it had to be against a team like Swansea.
"You either let them play or have a go, which we did. I thought Shefki Kuqi ran himself into the ground.
"While Julian Speroni's save from Jason Scotland at 2-1 was a match-winning save."
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