Sanchez's brace yesterday -- the second a beauty from Jack Wilshere's superb pass -- added to Shkodran Mustafi's first ever away goal for the Gunners was just enough to get them past the Eagles in Wenger's 810th Premier League game as a manager.
James Tomkins's 89th minute header -- Andros Townsend had drawn them level at 1-1 early in the second-half before Sanchez's scoring burst -- ensured a nervy finish, but the Gunners deserved to run out winners and end Palace's eight- game unbeaten run.
Palace were able to apply some pressure during the opening stages, the closest they came to testing Petr Cech came when Yohan Cabaye shot narrowly wide from 20 yards out.
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.
The ball was played back towards the right side of the area where Alexandre Lacazette drew a good save from Julian Speroni only for the ball to fall to Mustafi who finished neatly with a first time shot.
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.
It also made the winger a target for some robust treatment with Callum Chambers booked for pulling him back.
Zaha made the point he believed he deserved more protection too vigorously to referee Michael Oliver as they left the pitch at half time and could have been sent off after sarcastically reacting to the match official's decision to show him a yellow card.
At that point Palace were in the ascendancy but Sanchez's quick double soon killed off the home side's hopes.
The first came after Chambers played a deep ball into the home penalty area that was controlled by Sanchez before the Chile international exchanged passes with Lacazette and drilled the ball past Speroni.
Then four minutes later, the forward had his second after collecting Wilshere's long ball over the top with his first touch and finishing with his second.
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