Goals from Cardiff's former loanee Wilfried Zaha, who was jeered on his return to Wales, Michy Batshuayi and Andros Townsend sealed the home side's fate after they were given brief hope by a comical own-goal equaliser by Martin Kelly.
Bobby Reid hit back in stoppage time but the goal came too late to make a difference.
Cardiff's chances were not helped by an early injury to influential Victor Camarasa, who limped off after just 11 minutes.
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Zaha opened the scoring on 28 minutes before Kelly sliced the ball past his own keeper three minutes later. But Batshuayi restored Palace's first-half lead after rounding off a clever move with Jordan Ayew.
Cardiff rallied after the break with Josh Murphy and Kenneth Zohore both going close, and Kelly clearing another Murphy effort off the line. The misses highlighted Cardiff's major deficiency this season when they have consistently come up short in front of goal.
Palace soon made them pay, with Townsend bursting from the halfway line to shoot in off the post after 70 minutes as Palace won for the fifth time in six away league games.
This is the second time in five seasons Cardiff have gone down after just one campaign and the third time manager Neil Warnock has experienced a top-flight drop.
"Hopefully we can bounce back," said Cardiff captain Sean Morrison. "The fans can see how much effort we've put in - it's nice to know they've got our backs.
"We would've loved to have taken it to the last day. We've fallen short today and over the season and we're relegated because we didn't do enough over the year. We've lacked a bit of quality."
(Reporting by Neil Robinson; Editing by Christian Radnedge and Pritha Sarkar)
