Palace led through Andros Townsend’s close-range finish, doubling their lead when Yohan Cabaye’s shot looped in.
Luka Milivojevic clinched victory with a firm, low penalty as Palace moved six points clear of the relegation zone.
Sixth-placed Arsenal did not manage a shot on target in a poor second half.
Some travelling Gunners fans again called for manager Wenger, who has led Arsenal to top-four finishes in each of his previous 20 seasons at the helm, to leave the club.
The Frenchman’s side are seven points adrift of fourth-placed Manchester City with eight games remaining.
Feeble Arsenal put more heat on Wenger
The manner of Arsenal’s performance – disorganised, devoid of attacking ideas and lacking fight – will increase the scrutiny on Wenger yet again.
The 67-year-old has already faced protests from some supporters urging him to leave, with more calls clearly audible – along with the barracking of his players in the latter stages – at Selhurst Park.
Wenger’s contract expires at the end of the season and the club has offered him a new two-year deal, although he is still to announce whether he intends to carry on.
Arsenal had 72% possession against Palace but that mattered for little as the hosts broke quickly on the counter-attack, exploiting space down the flanks and taking their chances clinically.
The Gunners looked defensively vulnerable whenever Palace went forward, lacking leadership without injured captain Laurent Koscielny.
And when the visitors did attack, Palace keeper Wayne Hennessey was only required to make saves from Mohamed Elneny and Alexis Sanchez.
After the break, Hennessey did not even face a shot on target as Arsenal suffered a fourth straight away defeat for the first time under Wenger.
“Palace wanted it more. You could sense that from the kick-off,” Theo Walcott, Arsenal’s stand-in captain, said.