Laurent Koscielny exploited slack checking to head the hosts into an early lead from Sanchez's cross.
The Chile universal then completed off a slick move with Tomas Rosicky to twofold Arsenal's lead before half-time.
Sanchez, 26, included his second objective of the diversion and eighteenth of the season from a free-kick not long after the break.
It demonstrated a moderately standard triumph for an Arsenal side and for David Ospina, who held his spot after the 2-0 FA Cup third round win over Hull.
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It was the 26-year-old Colombia global's his first Premier League begin, with Wojciech Szczesny dropped to the seat taking after reports he was found smoking in the showers after the New Year's Day rout at Southampton.
Stoke were given early cautioning of Arsenal's aim when Sanchez and Tomas Rosicky constrained goalkeeper Asmir Begovic into recoveries in the opening five minutes.
What's more inside 60 seconds Koscielny exploited Arsenal's third corner of the match by heading in Sanchez's conveyance.
Armory were compelled to substitute safeguard Matthieu Debuchy when he disengaged his privilege bear in a test from Marko Arnautovic and impacted the promoting sheets behind the objective.
Stoke made little all through the amusement and their first genuine chance came when Glenn Whelan bursted a savvy free-kick from Bojan over the bar on 25 minutes.
Subside Crouch additionally headed an agreeable exertion wide from an Arnautovic cross.
Sanchez then extended Arsenal's lead with his seventeenth objective of the season - a low shot into the base left-hand corner after a keen one-two with Rosicky on the edge of the zone.
Not long after the break, Sanchez was among the objectives once more. His free-kick crushed through the divider and Begovic was not able to stop the ball go too far by means of his body and a post.
By then, the amusement was over as a challenge yet Stoke mobilized.
Geoff Cameron had an objective discounted for offside when he strayed in front of the Arsenal guard from Crouch's flick-on.
Furthermore, as full-time approached, substitute Stephen Ireland constrained Ospina into his just genuine recovery of note with a low right-foot exertion.
Weapons store chief Arsene Wenger addressing Match of the Day: "We had a solid begin and we realized that was essential today.
"Alexis Sanchez is one of the best players. He's a contender with a blend of ability and battling soul which is exceptionally hard to discover.
"He plays with energy and you need individuals to appreciate what they're doing on the pitch and reveal to it also."
Stoke administrator Mark Hughes identifying with Match of the Day: "We have a feeling that we could've improved.
"We got off to a poor begin and fell behind right on time. Our certainty wound down from that point on and we were a smidgen slower in our work and our focus.
"We never got to grasps in wide ranges truly and manage the ability Arsenal have approaching. We were well-beaten on the day and we can have no grumblings."
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