Shkodran Mustafi opened the scoring for the visitors with a tidy finish in the first-half, only for Andros Townsend to equalise shortly after the interval.
Townsend’s goal seemed to change the game, with Wilfried Zaha looking lively and Palace increasingly dangerous on the break.
However a quick-fire double for Sanchez killed the game and sealed all three points for Arsene Wenger’s side.
And while the Chile international will feature heavily in the headlines, Wilshere is also deserving of some plaudits after his assist ripped Palace’s defence in two for Sanchez’s second goal.
Wilshere picks the ball up in Arsenal’s half, before spotting Sanchez’s run and launching an inch-perfect pass which left Julian Speroni with little chance.
Arsenal face a tough trip to the Hawthorns to take on West Brom next.