The uninspiring contest seemed destined to finish goalless as Arsenal struggled to find the fluidity in the final third to break down a Stoke side that appeared to come with the sole intention of frustrating their opponents.
But after Andy Wilkinson gave away a poor free-kick on the edge of the box, substitute Podolski drilled a low free-kick that deflected off the boot of Geoff Cameron and wrong-footed Asmir Begovic in the Stoke goal.
There was some initial confusion as the referee’s assistant appeared to flag to disallow the goal and Arsenal players steamed over to the sidelines to vehemently remonstrate with the official. But, while Theo Walcott had been offside from the free-kick, there was clearly no interference with play and referee Chris Hoy was right to overrule his assistant to the relief of the majority inside a previously subdued Emirates.
It would have been an enormous relief too for manager Arsene Wenger, who knows every point is likely to be vital in the battle for a Champions League place.
Stoke proved difficult opponents, with manager Tony Pulis appearing determined to avoid the Potters losing an 11th straight time against Arsenal on the road. Until they went behind, Stoke piled every man behind the ball behind with the exception of the lone and isolated front man Peter Crouch. Stoke’s tactics were rudimentary as they sought to hit the tall striker with high balls whenever in possession, although frequently the attempts were wayward.
Stoke’s single effort on target throughout the 90 minutes spoke volumes for their lack of attacking threat.
But Arsenal were given a challenge to break Stoke down and they were largely unimpressive in trying to do so.
With Santi Cazorla and Podolski starting on the bench, Walcott looked the player most likely to make something happen, but all too often, particularly in the first half, he was wasteful with his final product.
Arsenal’s first two meaningful attempts at goal came, surprisingly from set pieces. Alex Oxlade-Chamberlain perhaps should have done better as a corner ran through to him at the back post but after chesting down he fired too close to Asmir Begovic who made a good save.
Stoke were uncharacteristically caught out from another corner minutes later when Olivier Giroud was allowed a free header, but oddly tried to direct the ball back across goal. After the ball was partially cleared, it arrived back into the box and Begovic was again forced to make a good save, this time from Laurent Koscielny’s header.
The one time Arsenal truly carved Stoke open came as Jack Wilshere caught out the visitors’ defense with a fine ball to find Oxlade-Chamberlain down the left of the box, but Begovic made a fine stop to prevent the midfielder’s curling shot from finding the far corner.
If anything, Arsenal, despite having two-thirds of possession, struggled even more to create opportunities after the break.
Nacho Monreal was solid on his debut from Arsenal, although he will rarely have an easier day defensively than he enjoyed against Stoke. Going forward he came close to creating an opportunity for Giroud with a chip to the back post, but Robert Huth was alert to prevent the striker from having a simple chance.
Cazorla and Podolski were brought into the fray after 68 minutes and the Spaniard was instantly heavily involved in trying to provide the breakthrough. But just 10 minutes later it was Podolski that provided the game’s crucial moment.
Cazorla came close to making the score line comfortable but was denied by another excellent Begovic save.
Arsenal were far from their best, but Stoke can have little complaint about the score line after a performance that so desperately lacked any ambition.