Owen Coyle's injury-hit defence couldn't cope in the first half as a towering header from the giant Ryan Shawcross and an own goal by Stephen Jordan gave his team a mountain to climb.
But Burnley outplayed their hosts for long spells in the second period and were unfortunate not to reduce the arrears.
The visitors held their own in the early exchanges and Robbie Blake threatened when his 18-yard strike was held by Thomas Sorensen in the 17th minute.
But Ricardo Fuller weaved his magic, leaving three defenders in his wake, before winning a free-kick which led to Stoke taking a 19th minute lead.
Liam Lawrence stood the ball up with a super delivery from the left edge of the penalty area and Shawcross powered a perfectly placed header inside Brian Jensen's right-hand post.
Burnley responded positively as Wade Elliott lifted a shot over at the near post and the visitors also had a couple of shouts for penalties for handball.
But the Clarets were really up against it in the 33rd minute when a trademark long throw from Rory Delap forced an own goal from Jordan.
Delap's delivery was aimed like a dart towards the near post and the ball skimmed off the side of Jordan's head to leave Jensen without a hope.
It was almost three and game over shortly afterwards when Jensen came for and failed to get a ball which Fuller sent towards goal with a looping header.
The Stoke striker was preparing to wheel away in celebration before Clarke Carlisle raced back to clear with a bicycle kick from under the crossbar.
To their credit, Burnley showed tremendous character at the start of the second half and forced Stoke to defend in depth.
Shots by Wade Elliott and Blake were charged down close to goal before Sorensen made a couple of fine saves to deny Blake and Steven Fletcher.
Stoke were on the rack and manager Tony Pulis responded by replacing a tiring James Beattie with Dave Kitson in an attempt to pep up his troops.
Kitson soon rattled the crossbar with a thunderous effort, but a third goal would have been extremely tough on Coyle's battlers.