Michy Batshuayi opened the scoring for the Eagles five minutes before the halftime break with his first goal for the club.
Johnny Evans restored parity midway in the second half, turning home a cross from Harvey Barnes.
Wilfred Zaha restored Palace's lead in the 70th minute with a close-range finish with his eighth goal of the campaign.
Luka Milivojevic netted the visitors' fourth goal from the penalty spot with nine minutes remaining, before Zaha rounded off the scoring in second-half stoppage time with his second goal of the game.
Newcastle United 2-0 Huddersfield Town
Huddersfield Town's survival bid took another dent with a 2-0 loss to Newcastle United at the St Jame's Park.
Earlier in the first half, Huddersfield's Tommy Smith received his marching orders for an off-the-ball challenge.
Second-half goals from Ayoze Perez and Solomon Rondon saw the Magpies continue their resurgent quest which results in elevation from 15th place elevation on the table.
AFC Bournemouth 1-1 Wolverhampton Wanderers
Bournemouth and Wolves played to a 1-1 draw at the Vitality Stadium in a match marred with penalties,
Both the goals from either side came from the spot, with Josh King striking after 13 minutes while Raul Jimenez converted three minutes from the full-time whistle.
Bournemouth were awarded a second penalty late on but King failed to convert as the encounter finished 1-1, with the Cherries moving from 10th to 11th while Wolves drop from seventh to eight.