Olivier Giroud made sure of the points as he headed home Aaron Ramsey's cross with just a couple of minutes left.
Palace caretaker boss Keith Millen, who had taken over following Ian Holloway's departure on Wednesday, had set up his side to stifle Arsenal, and it worked as they saw out the opening 45 minutes.
However, Arsenal claimed the lead just minutes after the re-start as Adlene Guedioura recklessly slid in on Serge Gnabry and Arteta slotted home the resulting penalty.
Arteta was at the centre of the action as he then saw red for hauling down Marouane Chamakh when he was the last man, although the Palace striker still had some way to go before getting in on goal.
Palace looked to take advantage of the extra man, and they tested Wojciech Szczesny on a couple of occasions before the game was settled by Giroud.
There was a positive start by Arsenal, with Giroud heading over a cross from right-back Bacary Sagna.
The visitors, though, had to make an early change when Mathieu Flamini pulled up with what looked like a groin problem and was replaced by Gnabry.
After dropping off for much of the opening 15 minutes, Palace found some energy when Jerome Thomas - once on the books at Arsenal - darted down the left and his deep cross was headed over by Barry Bannan.
Arsenal were soon back on the offensive as Gnabry played in Mesut Ozil, but he looked to square the ball through the six-yard box instead of shooting.
Chamakh - sold by Arsenal in the summer - tested Szczesny with a dipping 20-yard effort as the Eagles again looked to take the match to the Premier League leaders, with Bannan's curling cross then just ahead of Damien Delaney.
Santi Cazorla almost had Arsenal in front when the Spaniard spun onto an angled pass through the Palace box and sent a low shot across the face of Julian Speroni's goal.
The Palace goalkeeper then stood up well as Ramsey got in at the near post to drill an angled shot at point-blank range.
Arsenal had a penalty claim denied just before half-time when Delaney bundled over Gnabry right on the chalkline. Both referee Foy and his assistant signalled for only a free-kick, which came to nothing.
There was no debating a key decision at the start of the second half when Guedioura cut down Gnabry, and this time all the officials were in no doubt.
Arteta crashed the penalty past Speroni, into the left corner, to give the leaders some breathing space.
It was almost 2-0 straight away when a clearance from Delaney bounced off Gnabry and just an inch past the post.
Arsenal were reduced to 10 men after 65 minutes. A long ball up-field was taken on the chest by Chamakh, who looked to get clear before tussling with Arteta, shoulder to shoulder just inside the Arsenal half.
The pair went down in a heap, but that was enough to convince Foy the Gunners captain had denied his former team-mate a clear goalscoring opportunity and he went for the red card.
Wenger replaced Gnabry with Jack Wilshere as he looked to protect the slender lead before, after 72 minutes, Spain defender Nacho Monreal came on for Cazorla.
Szczesny made two brilliant saves to keep Arsenal ahead when he first touched a thunderous 20-yard effort from Joel Ward against the goal frame and then, from the resulting corner, produced a brilliant one-handed stop to turn over a dipping strike from Mile Jedinak.
Monreal, deployed on the left of midfield, ghosted into the penalty area with some fine close control, before his shot at the near post was blocked. Then Ozil's acrobatic effort only just fizzed over the bar.
Arsenal finally secured three points when Ramsey broke down the left and delayed a chipped pass through for Giroud, who arrived on cue to nod the ball past Speroni.