The in-form Aaron Ramsey, Per Mertesacker and Bacary Sagna found the target for the Gunners - who have now enjoyed four successive victories in the league and seven in all competitions - with Geoff Cameron's first goal in English football proving to be scant consolation for the Potters.
It took just five minutes for Arsene Wenger's side to break the deadlock, with Asmir Begovic only able to parry a Mesut Ozil free-kick into the path of Ramsey - who reacted quickest to stroke into the back of the net.
Stoke have caused Arsenal problems in the past, though, and restored parity on 26 minutes when Marko Arnautovic saw a volley crash back off the post and Cameron was on hand to expertly roll the ball past a sprawling Wojciech Szczesny.
Mertesacker came close to restoring the home side's advantage on the half-hour mark, as he saw an effort cleared from in front of the line, but he did not have to wait long before making a telling contribution.
Ozil swung over a corner from the right and his fellow Germany international, meeting the delivery at the near post, was able to send a header which looped over Begovic and Laurent Koscielny into the bottom corner.
Arsenal's third, which arrived on 72 minutes, was almost an exact replica of their second, with another set-piece from Ozil met by another floated header - with Sagna netting for the first time in 19 months.
Wenger was forced into a late change to his starting XI when England forward Theo Walcott suffered a minor abdominal strain during the warm-up and was replaced by German youngster Serge Gnabry.
Denmark striker Nicklas Bendtner was on the bench for the first time this season, having seen a move away during the transfer window blocked.
It did not take long for a summer arrival in north London to have an impact on his home debut, with Ozil's 20-yard curling free-kick parried out by Begovic and Ramsey was first to the loose ball to slot home.
To their credit, Stoke slowly grew into the match and were level on 26 minutes.
Arsenal's defence were caught square by a deep ball through the penalty area from Steven Nzonzi on the right and Arnautovic crashed his volley against the base of the far post. The rebound fell back out to United States defender Cameron, who kept his effort low to beat Szczesny in the bottom right corner.
Arsenal were soon back on the offensive, and it was 2-1 on 36 minutes.
Ozil's corner from the right was flicked on at the near post by Mertesacker. His header dropped inside the far corner where Koscielny had looked to get the final touch in front of the goalkeeper.
At the start of the second half, Gnabry - another German hoping to impress watching national-team manager Joachim Low - was flattened by Robert Huth as Arsenal broke quickly.
Referee Mike Dean played a good advantage as Olivier Giroud got clear to fire in a shot from 20 yards which was palmed over by Begovic before Huth was shown his due yellow card.
Arsenal made sure of the three points and top-spot in the Premier League when, on 72 minutes, Ozil's deep free-kick was headed back over Begovic and into the far corner by defender Sagna.
With the result safe, Wilshere - who had endured plenty of tough challenges all afternoon - was given a rest, replaced by Spain defender Nacho Monreal.
Ozil was substituted himself shortly afterwards, leaving to a standing ovation, as midfielder Mikel Arteta made his first appearance of the season after a thigh injury - and on this evidence, the German playmaker could well give Arsenal fans more to cheer about before the medals are handed out in May.