Wenger's side gradually took charge and they forced the breakthrough in the 24th minute when Palace's failure to clear Mesut Ozil's free-kick eventually led to Mustafi's opening goal.
Crystal Palace had been undefeated in its last eight games and, though it next hosts Manchester City, it again demonstrated it can survive by often resisting Arsenal and going level with Andros Townsend's goal.
Palace showed no sign of getting to grips with Arsenal, but they managed to avoid falling further behind before the break - Ozil tried to square to Sanchez when through on goal, only to get it all wrong.
Defender Calum Chambers was recalled for clash as Arsenal switched to a back three
For much of the game, Arsenal produced some of the fine football we have grown accustomed to since Wenger's arrival in 1996, and Sanchez produced two moments of real quality in less than four second-half minutes to clinch all three points as the Gunners boss moved level with Alex Ferguson in terms of Premier League fixtures managed.
With a brilliant chipped-pass from inside his own half, Jack Wilshere - often a peripheral figure this season - sent Sanchez into space in the Palace area and, after he impressively controlled, the Chilean routinely poked beyond Speroni.More news: Miss America President Reportedly Resigns After CEO's Vulgar Emails Surface
But as full-time drew nearer, Palace perked up and Arsenal sat deeper, so it was not entirely surprising that James Tomkins nodded in a livener with four minutes of injury-time still to play. He drags it down the outside of Schlupp, checks back leaving his man for a burton, and curls a shot that Speroni can only push back into play, and Mustafi confidently strokes home.
Wilfried Zaha was Palace's most threatening player throughout the first half with the Ivorian maintaining the form that has seen him linked with a number of top clubs this season.
Crystal Palace's unbeaten run came to an end with a 3-2 defeat at home to Arsenal.More news: Tokyo flight turns back after passenger 'boards with wrong ticket'
"I can only repeat what I've said until now and I've said it many times, so I won't repeat". Out of nothing, this match is duhn!
89' - GOAL! Crystal Palace 2-3 Arsenal (Tomkins) Over comes the corner and at the back post, Tomkins climbs above Koscielny to head down and in!More news: Russian Federation claims U.S. training former ISIS fighters in Syria
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