Arsenal climbed above neighbours Tottenham and into fifth place in the Premier League with a dominant display against Stoke.
Laurent Koscielny took advantage of slack marking to head the hosts into an early lead from Sanchez’s cross.
The Chile international then finished off a neat move with Tomas Rosicky to double Arsenal’s lead before half-time.
Sanchez, 26, added his second goal of the game and 18th of the season from a free-kick shortly after the break.
It proved a relatively routine victory for an Arsenal side and for David Ospina, who retained his place after the 2-0 FA Cup third round win over Hull.
It was the 26-year-old Colombia international’s first Premier League start, with Wojciech Szczesny dropped to the bench following reports he was caught smoking in the showers after the New Year’s Day defeat at Southampton.
Stoke were given early warning of Arsenal’s intent when Sanchez and Tomas Rosicky forced goalkeeper Asmir Begovic into saves in the opening five minutes.
And within 60 seconds Koscielny took advantage of Arsenal’s third corner of the match by heading in Sanchez’s delivery.
Arsenal were forced to substitute defender Matthieu Debuchy when he dislocated his right shoulder in a challenge from Marko Arnautovic and collided with the advertising boards behind the goal.
Stoke created little throughout the game and their first real chance came when Glenn Whelan blazed a smart free-kick from Bojan over the bar on 25 minutes.
Peter Crouch also headed a tame effort wide from an Arnautovic cross.
Sanchez then stretched Arsenal’s lead with his 17th goal of the season – a low shot in to the bottom left-hand corner after a smart one-two with Rosicky on the edge of the area.
Soon after the break, Sanchez was among the goals again. His free-kick squeezed through the wall and Begovic was unable to stop the ball crossing the line via his body and a post.
By then, the game was over as a contest but Stoke rallied.
Geoff Cameron had a goal ruled out for offside when he strayed ahead of the Arsenal defence from Crouch’s flick-on.
And, as full-time approached, substitute Stephen Ireland forced Ospina into his only real save of note with a low right-foot effort.