First-half goals from Santi Cazorla and Olivier Giroud saw Palace condemned to defeat against Arsenal at Selhurst Park, although they nearly snatched a point in injury-time.
The visitors got off to a good start when the Spanish midfielder converted from the spot just nine minutes in, and Giroud netted just before half-time to give the Eagles a mountain to climb in the second half.
Alan Pardew's side rallied and created some good opportunities in the second half, and after Glenn Murray found what seemed like a consolation with a minute to go, the striker thumped the post with a header less than a minute later in what was an incredible ending in SE25.
However Palace would have felt hard done by for the opening goal as the visitors were awarded a penalty on eight minutes. Making his Premier League debut, Pape Souare was caught in possession by Danny Welbeck and a clumsy challenge by the Eagles left-back brought the England international down on the edge of the box, for which Arsenal were awarded a spot-kick.
Replays suggested the foul took place outside the box but nevertheless, Santi Cazorla stepped up and stroked the ball into the opposite corner to Julian Speroni's dive to take the lead.
It took Palace a while to get into their stride against the Gunners and despite having a lot of the ball in their opponents' final third, they couldn't create anything from open play in the first quarter of the game, with a Dwight Gayle free-kick which flashed over the crossbar the closest they came to testing David Ospina.
Having not played well, they nearly made it into the break just a goal down but on the stroke of half-time the Gunners doubled their lead. Alexis Sanchez slid the ball through a gap in the Palace defence for Welbeck to chase, and after his first-time shot was parried by Speroni Olivier Giroud was on hand to tap the rebound into the net and hand Arsene Wenger's men a cushion at the interval.
Six minutes after the restart and Palace's bar was struck when Sanchez drifted over a cross for Mesut Ozil whose looped header clipped the crossbar, although Speroni had it covered, and Jason Puncheon went close with a shot in the area which deflected off a Gunners defender and went narrowly wide.
There was a let-off for the Eagles just before the hour mark when a counter-attack saw Ozil in acres of space and he found Sanchez who stabbed the ball past Speroni but watched it trickle past the far post, but at this point if Palace could have nicked a goal they would have found themselves back in the game and they began to enjoy their brightest period of the game.
Firstly Wilfried Zaha managed to find Jordon Mutch on the edge of the box with a cross but it was slightly too high for the midfielder who volleyed over. They kept pressing and Souare nearly made up for his earlier effort when he forced his way past Calum Chambers and whipped over a cross from the byline which was met by a leaping Gayle but he headed the ball just over the top.
And Puncheon was a whisker away from converting a free-kick from inside the D with Ospina ready to pick the ball out of his net but there wasn't quite enough curl from the winger to hit the target on 73 minutes.
Palace kept going and Yannick Bolasie embarked on a powerful run through the heart of the Gunners midfield but shot tamely at Ospina.
However in injury-time the hosts scrambled home a late strike when a corner was lobbed into the area and headed back into danger by debutant Shola Ameobi, and after a Zaha shot was blocked Murray was on hand to score his first goal at Selhurst Park in 23 months.
There was time for one final attack and Bolasie burst down the left and whipped in a cross which Ospina missed with a punch and Murray attacked, and struck the base of the post with a header as Arsenal scurried out of south London with their three points in tact.
Palace: Speroni, Ward, Dann, Delaney, Souare, Zaha, Mutch, Ledley (Ameobi 79), Puncheon, Gayle (Murray 79), Campbell (Bolasie 56). Subs not used: Hennessey, Hangeland, Kelly, Jedinak.
Arsenal: Ospina, Monreal, Mertesacker, Koscielny, Chambers, Coquelin, Cazorla, Ozil, Sanchez (Gabriel 89), Welbeck (Gibbs 76), Giroud. Subs not used: Szczesny, Bellerin, Rosicky, Wilshere, Walcott.