A 78th-minute goal by striker Lukas Podolski proved the winner as Arsenal moved towards the Champions League places.
The first half took some time to gather momentum, but the home side began to dominate and were denied several times by Stoke goalkeeper Asmir Begovic.
It took until the 78th minute for Arsenal to take the lead, with Lukas Podolski seeing his free kick deflected home.
The game began in a lively fashion, with Bacary Sagna and Theo Walcott linking up well on the right, although the latter’s early pull-back could not find a team-mate in the area.
However, things calmed down rapidly into a familiar rhythm as Arsenal dominated possession but found themselves unable to create further chances as the away side held firm.
As the half went on, Stoke began to see more of the ball, with Peter Crouch looking threatening up front.
It took until the 32nd minute for either side to create an opening, and it fell to Arsenal, with Alex Oxlade-Chamberlain denied by Begovic’s superb reflexes after a corner.
The home side then created another opening a couple of minutes later, with Laurent Koscielny seeing his header blocked well again by the impressive Begovic.
Oxlade-Chamberlain was then denied again by the Bosnian as he latched onto a superb through-ball from Jack Wilshere but saw Begovic deflect his finish away for a corner.
However, despite the home side dominating possession and carving their opponents open, they were unable to force any more openings and went into half-time deadlocked at 0-0.
The second half began in a similar fashion, with the home side monopolising possession and toying with their opponents, but they were unable to create an early chance.
It took until the 53rd minute for the Gunners to create an opening, and it came through debutant Nacho Monreal, who sent in a teasing cross after some superb interplay but saw the ball cleared.
Then, just a minute later, Arsenal had another chance as Olivier Giroud nearly got on the end of a ball from the superb Wilshere but could not quite make good enough contact.
The Gunners were dominating possession as their opponents seemed unable to get the ball out of their half, but were struggling to create another chance to the frustration of their fans.
However, in the 78th minute Arsenal finally made the breakthrough as Podolski saw his free kick deflected home by Geoff Cameron, with the goal standing despite some suspicion of offside.
This seemed to galvanise the Gunners, who could have had a second through Santi Cazorla, who saw his shot tipped just over the bar by Begovic, but they held on to secure the win.