The Gunners, who moved up to fifth in the table, never looked in danger from the moment Laurent Koscielny headed home an Alexis Sanchez cross on six minutes to give them the lead.
The lead was doubled just after the half hour mark as man of the match Sanchez played a combination of one-twos with Tomas Rosicky before darting into the box and drilling home low to Stoke keeper Asmir Begovic’s right for his twelfth Premier League goal of the season.
The visitors had very few efforts of note, the best coming from former Three Lions striker Peter Crouch – who firstly fired tamely at goalkeeper David Ospina and then headed wide in additional time at the end of the first half.
Walcott came off the bench for Arsenal
Oxlade-Chamberlain, who had come close to scoring twice in the first half with a low fizzing strike before sending an effort just over the bar, was fouled by Steve Sidwell on the edge of the box four minutes after the half time break.
The Chilean Sanchez stepped forward to fire the ball through the wall, albeit with a slight deflection, and inside the near post despite Begovic getting two hands to it the make it 3-0.
With the contest seemingly over, Oxlade-Chamberlain was then replaced by another England international Theo Walcott as the forward continued his comeback from injury.
With ten minutes left Walcott was presented with an ideal opportunity to get his name on the scoresheet when played clean through by Sanchez, but he dragged his shot wide of the post.
Despite further efforts from the sublime Sanchez, Arsenal were unable to add to their advantage but will draw confidence from such a comprehensive performance against a side they have often come unstuck against in recent years.
'He is amazing. He shows it week in, week out'
Oxlade-Chamberlain on Sanchez
Ryan Shawcross, who has one cap for England, was in the Stoke defence and Under-21s goalkeeper Jack Butland was an unused sub for Mark Hughes' side.
Following the game, Oxlade-Chamberlain saluted his team-mate Sanchez for his performance.
He told Sky Sports: "He is amazing. He shows it week in, week out and I think that's the most important thing.
"For the top players it's about consistency and not just about being good one week but every week. And I think Alexis has done that all the way through this season.
"He was brilliant again today, got two good goals and set Laurent's goal up as well. Hopefully it continues for him because he's having a great season and his confidence is brimming and that helps the team as well."
Dusan Tadic celebrates his winner at Old Trafford
In Sunday’s late kick off there were no less than eight senior internationals on display as Southampton shocked Manchester United at Old Trafford.
The Saints picked up their first league victory at United in 27 years to move up to third in the table.
Louis van Gaal's side, which included England regulars Chris Smalling, Phil Jones, Michael Carrick and Wayne Rooney, did not register a single shot on target as their 10-match unbeaten run came to an end. Luke Shaw also started for the Red Devils, but he was replaced by U21 international Tyler Blackett after picking up an injury in the second half.
Dusan Tadic scored the only goal of the game when he tapped in calmly from 12 yards after Graziano Pelle's effort rebounded back off the post.
Fellow Three Lions Fraser Forster, Nathaniel Clyne and Ryan Bertrand, who won his two caps back in 2012, all excelled for the visitors, as did Under-21 midfielder James Ward-Prowse.
Harrison Reed, a regular in Aidy Boothroyd’s England U20 squad, appeared as a substitute for the final ten minutes.
Following the game, United and England captain Rooney told Sky: "That is football, that is how it goes. I think overall we had the better chances and played the better football and deserved to win but we were punished.
"I have seen Southampton play better, we stopped a lot of their threats but we got punished. We have to move on and focus on the next game."
