The Gunners dominated possession for much of the game and had considerably more efforts on goal, but do these statistics tell the full story?
Here, Sports Mole offers some analysis on the match.
On target 5
On target 1
Was the result fair?
A fairer reflection of the match would have been Arsenal winning by a bigger margin. Begovic kept Stoke in the game during the first half, twice denying Alex Oxlade-Chamberlain and keeping out Laurent Koscielny's close-range header. Stoke are to be commended for their tight defending, but Wenger's men should have killed them off far earlier than they did.
The Gunners were by far the better team today, but need to work on converting more of their chances and getting the ball forward more quickly. Although Stoke barely got a look in, a stronger team would likely have punished them for their wastefulness.
Tony Pulis's men were watertight at the back and Begovic played like a man possessed in the first half, but they were second best in every other area. Starting with Peter Crouch as a lone striker simply didn't work because they were unable to get any crosses in to the big man.
Sports Mole's man of the match
Asmir Begovic: There are a few contenders among the Arsenal side for this gong, but the Stoke goalkeeper is the man who turned what would otherwise have been a landslide victory into a competitive match.
A rather petty scuffle broke out involving a handful of players from each team after Mikel Arteta put in a tough tackle on Michael Owen. Tensions boiled over because referee Chris Foy was too lenient for much of the game, which brings us neatly on to our next area of focus.
Foy was far too lenient today and seemed reluctant to get his cards out whatever the offence. Ryan Shawcross escaped with a booking when he should have seen red for going in studs-first on Olivier Giroud late on, and Foy's lack of discipline led to that aforementioned scuffle at the death. However, the referee was right to overrule his linesman and allow Podolski's goal.
Arsenal: Arsenal take on Sunderland at the Stadium of Light in the Premier League next weekend.
Stoke: The Potters play host to struggling Reading in the league next weekend.