The attendance appeared well short of the stadium's 60,000 capacity as Arsenal left it until the final 15 minutes to score all three goals.
Pierre-Emerick Aubameyang scored the first two, including a penalty opener.
The Gabon striker added a second in the 86th minute, before substitute Alexandre Lacazette added a third from the spot. The success means Arsenal have finally won back-to-back Premier League games for the first time since November and continued their revival after a hard period in January and February. "It's a happy day for everyone - fans, players - and we feel very proud", Tottenham manager Mauricio Pochettino said.
Wilshere captained the home side, having been ruled out of England's recent friendlies against Holland and Italy due to an injury picked up while training with the national team.
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Stoke continued to take the game to the hosts, who were giving away possession cheaply.
Arsenal also came close with Aubameyang but his chip was denied by Jack Butland.
The Arsenal side this season so far, however, have been anything but invincible. Ospina looked sharp in goal despite the notable mistake he made while playing against France while on worldwide duty the week before.
Aubameyang then put the game beyond Stoke 11 minutes later, producing a lovely volley from just inside the area to find the bottom-right corner.
Pierre-Emerick Aubameyang opened the scoring from a penalty after Bruno Martins Indi was adjudged to have fouled Mesut Ozil, only for replays to show he won the ball.
Stoke gave Aubameyang too much space for a simple second goal in the 86th minute.