© PA Photos
The visitors were the first to force a save from the opposition keeper when Peter Crouch controlled Ryan Shawcross's long ball forward before unleashing a half-volley that Wojciech Szczesny needed to save.
The rest of the half was the Asmir Begovic show, however. The Stoke keeper denied Alex Oxlade-Chamberlain a golden opportunity from point-blank range before pulling off another fine save from Laurent Koscielny's back header.
Begovic was called upon again just before the break, denying Oxlade-Chamberlain for a second time with a fingertip save.
© AP Photos
Arsenal finally broke the deadlock with under 15 minutes of the match remaining as Podolski's free kick deflected off Geoff Cameron and into the net.
Santi Cazorla almost killed the game off 10 minutes from time after taking on the entire Stoke defence, but Begovic got a crucial touch to the Spaniard's close-range strike.