After securing just five points from as many Barclays Premier League matches, the Gunners were in danger of losing ground on the top four coming into the game. Arsene Wenger's side looked set for another frustrating day at the office - thanks in no small part to an outstanding display by Stoke goalkeeper Asmir Begovic.
However, substitute Podolski popped up 12 minutes from time with a low free-kick that deflected in off Geoff Cameron.
The Gunners made five changes for this match, with deadline-day signing Nacho Monreal handed his debut. The Spain international replaced the injured Kieran Gibbs at left-back in an Arsenal side that started much better than they had against Liverpool in midweek.
Robert Huth blocked early threatening balls from Theo Walcott and Jack Wilshere, before Alex Oxlade-Chamberlain, making his first league start since January 13, struck wide.
It took 15 minutes for Wojciech Szczesny to best tested by Stoke. Jonathan Walters' strike from distance was comfortably dealt with by the Poland international, who then watched a Peter Crouch snapshot deflect off Laurent Koscielny and out for a corner.
Begovic was the scourge of Arsenal once again in the 34th minute, denying a Koscielny header with another block. Four minutes from the break the Stoke goalkeeper was at it again. Wilshere played an exquisite through ball to Oxlade-Chamberlain, whose curled effort looked destined to ripple the net until Begovic superbly palmed wide.
Huth was called into action shortly after play resumed for the second half, rising well to stop Olivier Giroud bundling home a Monreal cross. Wenger brought on Santi Cazorla and Podolski in a bid to inject new life into his side's attack, with Diaby and Oxlade-Chamberlain replaced.
Glenn Whelan picked up a booking as City looked to hold off the hosts, who finally took the lead in the 78th minute. Andy Wilkinson received a yellow card for bringing down Walcott on the edge of the box, allowing substitute Podolski to send a low free-kick that deflected in off Cameron's heel.
It had looked like the goal would be chalked off for an apparent offside against Walcott, but, after consulting with his assistant, referee Chris Foy awarded the goal. Michael Owen, Kenwyne Jones and Cameron Jerome all came on for the final stages at Tony Pulis looked for a leveller, which never came.