Olivier Giroud's spectacular goal, a scorpion kick from Alexis Sanchez's cross, gave the Gunners the lead.
The host's dominance was evident throughout and they should have won by more, but had to settle for just a second - scored by Alex Iwobi, heading into the net following poor Palace defending.
Gunners boss proceedings
The hosts had the first chance of the game when Sanchez ran in behind Martin Kelly but had his effort blocked by James Tomkins. The resulting corner was dealt with much more conviction by the Eagles' defence.
Trying to assert authority, Arsenal should have gone ahead when Nacho Monreal's dangerous cross should have been converted by Giroud who somehow failed to make contact with the ball. Mohamed Elneny's effort was then blocked once again by Tomkins.
Arsenal were having huge joy on both flanks but their next attack came through the centre as Granit Xhaka's pass found Sanchez who turned and fired at goal, only to see his effort fly just wide of the impressive Wayne Hennessey's left-hand post.
Palace found themselves under heavy pressure in the first 20 minutes as the Gunners bombarded Hennessey's goal. Iwobi had his side's first effort on target when he guided Hector Bellerin's cut-back goalwards, forcing the Wales goalkeeper into a save low to his right.
Giroud wonder-goal separates sides in first half
After all the pressure, Arsenal finally found a route past Hennessey and the goal was of the very highest calibre. A Palace attack broke down, the Gunners countered and Sanchez's inch-perfect cross was met by a superbly improvised scorpion kick by Giroud. The ball, out of the reach of the stretching Hennessey, flicked off the underside of the bar and bounced over the line. A finished that made Henrikh Mkhitaryan's attempt a few days before look routine.
Palace still struggled to enter Arsenal's half in the period after the goal, perhaps shellshocked by the goal they had just conceded. Elneny almost made it two as his 25-yard drive whistled just past the post.
The Egyptian midfielder was controlling proceedings in the first half and his pass between Kelly and Scott Dann found Sanchez, whose cross eventually fell to the advancing Monreal but the Spaniard's swing at the ball was met by the linesman's flag.
The Eagles finally had their first effort of the game 36 minutes into the first half. Yohan Cabaye created space on the edge of the area but his tame effort was held comfortably by Petr Cech.
Arsenal carved open an inferior Eagles defence once more before half-time. A mix-up between Dann And Tomkins saw the former toe-poke to ball towards Iwobi six yards out, but Hennessey once against somehow kept the score intact. The goalkeeper then easily held Lucas Perez's effort from long-distance.
Iwobi secures Arsenal victory with headed second half effort
Palace started the second half much better than they did the first and almost found themselves level a minute after the break. Christian Benteke, anonymous in the first half, met Andros Townsend's cross but should have done better as his tame header trickled past the post.
The visitor's pressure didn't last long, though, as they failed to clear Arsenal's corner soon after and the eventually broke to Sanchez following pin-ball in the six yard box, but the Chilean's powerful effort was blocked by Dann.
The game appeared out of sight soon after when Monreal was given space on the left to cross, Dann deflected the ball upwards and Iwobi headed over Hennessey and into the net via Ward.
The goal seemed to motivate the visitors and they had three good chances in quick succession to halve the deficit. Benteke powerfully headed Puncheon's corner towards goal, only to find Cech in superb form. Cabaye then volleyed towards goal but Cech once again batted the ball away for a corner. The resulting kick fell to Benteke who should have scored.
The visitors had restored confidence and Townsend's in-swinging cross almost caught out the Arsenal goalkeeper who was forced to tip it away at the last minute.
Xhaka almost scored a spectacular third, dispossessing Jordon Mutch before trying to lob Hennessey from 45-yards, although the effort had deflected off Townsend and the ball went out for a corner which was easily dealt with.
As they game drew to a close, Giroud almost finished the job he had started when he was inches away from connecting to Sanchez's cross.
Arsenal should have had a third in added time when Sanchez set up sub Alex Oxlade-Chamberlain who found Hennessey at his best yet again.
Impressive Arsenal travel to Bournemouth on 3 January and will be full of confidence following this convincing victory. Sam Allardyce faces his first game at Selhurst Park the same evening as Palace welcome Swansea City to South London.