Arsenal took the lead in the 25th minute, when Shkodran Mustafi knocked in the rebound after Palace goalkeeper Julian Speroni turned aside a shot by Alexandre Lacazette on Thursday, reports Efe.
The Gunners created a fistful of solid chances before the half-time break, but none of them turned into goals.
Hector Bellerin came close to making it 2-0 in the first minute of the second half, instead Palace pulled level in the 50th minute with a goal by Andros Townsend.
But the joy of the Palace fans packed into Selhurst Park was short-lived.
Sanchez got his first of the night in the 61st minute, beating Speroni with a shot just inside the right post. The Chilean international struck again five minutes later, converting a perfect long ball from Jack Wilshere to give Arsenal a 3-1 advantage.
The hosts mounted a late charge and James Tomkins connected with a header in the 89th minute to narrow the deficit to one goal, but the Gunners hung on to collect all three points.
The win would have been especially satisfying for Arsenal's Arsene Wenger as he moved into a tie with Manchester United legend Sir Alex Ferguson for most Premier League matches managed: 810.
Despite having the same number of points as Tottenham, 37, the Gunners sit behind their North London neighbors and rivals in sixth place by virtue of Spurs' better goal differential.
On the bright side, Arsenal is only a point behind fourth-place Liverpool.
For Crystal Palace, who started the season with seven straight losses, the defeat marked the end of an eight-match unbeaten run. With 18 points, they are in 16th place, but just a point above the drop zone.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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