The pressure has been building on the Frenchman in recent weeks and a fifth defeat in eight league outings will do little to help his cause, with the Gunners seven points adrift of the top four with just the one game in hand still to play.
A third home victory in succession for a completely reformed Palace side was secured thanks to goals from Andros Townsend, Yohan Cabaye and Luka Milivojevic, the latter of whom tucked away from a contentious penalty to help move his team six clear of danger.
Milivojevic produced another commanding showing in front of the back four and even ventured forward at times, flashing one long-range effort narrowly wide from the first real attack of the match.
The Gunners' first sight of goal fell to another unlikely source, as Mohamed Elneny - again selected alongside Granit Xhaka in the engine room - guided the ball towards the far corner but was kept out by Wayne Hennessey.
There was not a great deal between the two unchanged sides in the opening 18 minutes or so of the contest, at which point the Eagles flipped the switch and found the opener through a belting finish from former Tottenham Hotspur winger Townsend five yards out.
Some good work from Wilfried Zaha created the goal, with the in-form wideman managing to pick out his teammate despite losing his footing when delivering the pass from out wide.
Arsenal failed to put together too much of a response in the remainder of the first half, coming closest to a leveller through a Shkodran Mustafi header in the dying stages after he directed the ball on target for Hennessey to routinely collect.
For all of Arsenal's threats, Palace created the next big chance as Christian Benteke - with two in two since the international break - was slotted through down the left but denied by a big Emiliano Martinez hand.
The Eagles, whose four-match winning run came to an end last time out at Southampton, started the second half the brighter and very nearly had a second goal.
Benteke was prevented just a third home goal this season by Hector Bellerin's fine block, before seeing the offside flag deny him a minute later after Townsend's initial shot was well kept out by Martinez.
It did not have the desired effect, though, because Palace were two up soon after thanks to a world-class finish from one-time Arsenal target Cabaye, lifting the ball over the reach of Martinez when picked out by an in-form Zaha.
A third soon followed after Martinez dived in on Townsend to concede a penalty - the England international perhaps making the most of it by looking for the contact - allowing Milivojevic to calmly tuck into the bottom corner.
Benteke struck a shot into Nacho Monreal late on and then saw another flash wide, as the Gunners slipped to an embarrassing fourth away defeat in succession for the first time under Wenger.