The Swans made four changes as Garry Monk recalled the fit-again Kyle Naughton, who recovered from an ankle injury, while Kyle Bartley and Marvin Emnes were also given the nod along with Leon Britton who made his first start since January.
Monk also included Kenji Gorre, who has impressed in the club's Under-21 side this season, on the substitutes bench for the first time where he was joined by Raheem Hanley.
Ashley Williams, Neil Taylor, Gylfi Sigurdsson and Jonjo Shelvey all missed the trip to Selhurst Park with slight knocks.
Wayne Hennessey, Joel Ward, Scott Dann, Brede Hangeland, Pape Souare, Wilfried Zaha, Mile Jedinak (capt), James McArthur (Glenn Murray, 35), Yannick Bolasie (Fraizier Campbell, 81), Jason Puncheon, Marouane Chamakh (Jordon Mutch, 65).
SUBS: Julian Speroni, Damien Delaney, Martin Kelly, Chung-Yong Lee.
SWANS: Lukasz Fabianski, Kyle Naughton, Federico Fernandez, Kyle Bartley, Jazz Richards, Leon Britton (Matt Grimes, 70), Jack Cork, Marvin Emnes, Nathan Dyer (Modou Barrow, 63), Jefferson Montero (Kenji Gorre, 83), Bafe Gomis.
SUBS: Gerhard Tremmel, Angel Rangel, Raheem Hanley, Jay Fulton.
The Swans boasted an impressive recent record at Selhurst Park, winning on their last three visits to South London without conceding a goal.
Palace, meanwhile, were still harbouring hopes of a top ten finish if they could claim victory and results elsewhere went their way, and they had the first effort on goal after ten minutes as Jason Puncheon shot over from just outside the box.
At the other end, Jack Cork saw a near post header comfortably saved by veteran Julian Speroni, while the lively Yannick Bolasie cut in from the left before seeing his low drive beaten away by Lukasz Fabianski at his near post.
Palace were forced into a first-half change ten minutes before the break as midfielder James McArthur was replaced by Glenn Murray.
Half-time: Crystal Palace 0 Swans 0
Neither side made any changes at the break, but Marvin Emnes had the first sight of goal in the second half as his low strike was well held by Speroni.
But Palace responded well as Glenn Murray saw a header saved by Lukasz Fabianski, before the hosts broke the deadlock just shy of the hour mark.
A long free kick into the box was met by Mile Jedinak and as the Palace skipper headed the ball back across goal, Marouane Chamakh was on hand to control and fire a left-foot past the keeper.
Both sides then traded substitutions as goal scorer Chamakh hobbled off with a hamstring injury, while Modou Barrow replaced Nathan Dyer for the visitors.
Palace, however, continued to pose the greater threat as Wilfried Zaha shot the wrong side of the right-hand post and skipper Jedinak saw a header saved by Fabianski.
The Swans introduced Matt Grimes off the bench in place of skipper Leon Britton, while youngster Kenji Gorre replaced Jefferson Montero as the winger made his Premier League debut.
But Palace held firm as Alan Pardew's side finished the season on a high while the Swans, despite defeat, can toast a fine season as they finished eighth in the table.