The France international scored on the verge of half-time after Santi Cazorla gave the Gunners the lead, though Glen Murray's last-gasp goal caused a nervy finish
The Gunners took an early lead through Santi Cazorla as the Spain midfielder slotted home from the penalty spot after Danny Welbeck was felled in the area.
And Olivier Giroud doubled the lead on the verge of half-time as he fired in his 50th goal for Arsene Wenger's side after Julian Speroni could only parry an effort from Welbeck.
Glen Murray pulled one back in stoppage time, but the visitors held on for the three points.
Arsenal - who were able to name Jack Wilshere in the squad for the first time since November after injury - were on the back foot early on as Palace threatened down the right through Wilfried Zaha.
They pressed Arsenal high up the pitch but sloppy play from Premier League debutant Pape Souare gifted the visitors an opportunity to lead.
Referee Mark Clattenburg felt the foul on Welbeck took place inside the box and, after the official had pointed to the spot, Cazorla expertly slotted home.
It proved the only real chance of the opening 20 minutes, with Alexis Sanchez almost forcing an opportunity soon afterwards as he pressured Scott Dann into losing possession, only for Speroni to come out and clear.
Palace, for all their promising spells of possession, struggled to test goalkeeper David Ospina and his defence before Arsenal made the most of their threat on the break when Giroud doubled their advantage.
A clever pass from Francis Coquelin found Welbeck and, when the England international's effort was saved, Giroud reacted quickest to register his 50th Arsenal goal in first-half stoppage time.
Mesut Ozil had Speroni worried with a looping header that flew over the crossbar early in the second half but, like in the first period, the game continued to see Palace have spells of possession against Arsenal's threat on the counter.
In a bid to get back in the game, home boss Alan Pardew introduced Yannick Bolasie from the bench for his 100th Palace appearance but, alongside the likes of Zaha, Jason Puncheon and Dwight Gayle, he failed to unlock the Arsenal defence.
Gayle could only angle Souare's header over the crossbar with 20 minutes left before Puncheon flashed a free-kick wide.
Substitute Murray - on as a 79th-minute replacement for Gayle - then almost single-handedly gained Palace a point, as he first poked home a shot inside the area before hitting the post with a diving header deep into stoppage time.
However, it proved a frustrating day for Pardew.