Sam Allardyce had lost 15 times to Wenger in the league previously but the hosts' resurgence under the former England manager continued with their fifth win in six games - which now includes the scalp of Arsenal having also beaten league leaders Chelsea.
Palace opened the scoring with their first shot on target, Andros Townsend turning in a low cross from his fellow winger Wilfried Zaha after Arsenal failed to deal with a long ball.
Zaha and Townsend were both involved in Palace's second goal too, with the former picking out Yohan Cabaye for a brilliant finish, and Luka Milivojevic converted a penalty for his first Premier League goal to complete an impressive victory over a limp Arsenal side.
Wenger's men have now lost four successive away Premier League games, conceding three goals in each, and their chances of qualifying for the Champions League - as they have every season under the Frenchman - are fading fast, with a seven-point gap to make up on fourth-placed Manchester City.
Palace's crushing win increases their cushion from the bottom three to six points, although they stay 16th, while Allardyce's men have a game in hand on the two sides immediately below them in the table, Hull City and Swansea City.
Milivojevic shot narrowly wide after six minutes as an unchanged Palace side made a bright start, before Wayne Hennessey turned a firm Mohamed Elneny drive around his right-hand post.
Under-pressure Wenger could then only sit and watch as Palace took the lead after 16 minutes.
Christian Benteke won a long Hennessey kick and Townsend and Cabaye combined to find Zaha on the right.
Despite the winger slipping as he delivered a low cross, Townsend arrived late to lift a clipped first-time finish past Emiliano Martinez on his 250th club football appearance.
Alexis Sanchez tested Hennessey and the Chilean bent another effort wide of the far post as Arsenal sought an immediate response.
But Palace continued to threaten and Benteke forced a sharp near-post save from Martinez after 41 minutes, with the resulting corner flicking narrowly wide via an Arsenal defender.
Danny Welbeck almost equalised for the visitors shortly before half-time when fed by Mesut Ozil but the striker's shot across goal went wide, then Hennessey easily claimed Gabriel's header.
Wenger had never before lost a Premier League game against Palace but the hosts had the ball in the net again five minutes after the interval, although a raised flag disallowed Benteke's rebound finish.
Olivier Giroud and Aaron Ramsey were introduced in a double switch from Wenger after 58 minutes but Palace soon added a second goal to take full control.
Townsend fed Zaha and, although the winger was again off-balance as he pulled the ball back, Cabaye's powerful dipping strike gave Martinez no chance.
485 - Yohan Cabaye has scored his first Premier League goal at Selhurst Park for 485 days (last one v Southampton in Dec 2015). Overdue.— OptaJoe (@OptaJoe) April 10, 2017
The Arsenal keeper then brought down Townsend in the box and Milivojevic beat him with a sweetly-taken penalty to nudge Palace closer to Premier League safety.
For Wenger the pressure continues to grow with another abysmal display doing nothing to keep the angry Gunners fans from pushing him closer to the Emirates' exit door.
Key Opta Facts:
- Arsene Wenger has suffered four consecutive away Premier League defeats for the first time as Arsenal manager.
- This is Arsenal’s worst away Premier League run since April 1995 (also four defeats in a row) when they were managed by Stewart Houston.
- Arsenal conceded three goals in four consecutive away league games for the first time since September 1929.
- Wilfried Zaha has had a hand in five goals in his last five Premier League games (two goals, three assists).
- In the last eight Premier League games, only Sunderland (6) have lost more games than Arsenal (5).
- Sam Allardyce won three consecutive home Premier League games for the first time since he was West Ham boss in December 2014.