The home team dominated early on with striker Andy Gray forcing a save out of Steve Simonsen inside the first 60 seconds.
A quick Robbie Blake free-kick after three minutes created a chance for Alan Mahon but he shot wide of the near post.
The game was still inside the opening five minutes when Simonsen had to make another save, this time from Kyle Lafferty.
John Eustace wasted a free-kick in a good position on the left-hand side of the penalty area by curling the ball harmlessly wide.
A brilliant save from Simonsen denied Mahon a spectacular goal after 37 minutes as the midfielder's 25-yard volley was pushed behind for a corner.
Stoke's best chance in the first half arrived just prior to the interval when Danny Pugh's cross found the head of Rory Delap who forced a save out of Gabor Kiraly.
Simonsen was quickly into the action in the second half saving a left-foot strike from Blake and an even better attempt from Chris McCann.
A quick counter-attack by the Clarets on 65 minutes carved out a chance for Kyle Lafferty but, after good work from Mahon and Blake, the Northern Ireland international shot over the crossbar.
The Clarets continued to press forward in search of the all elusive goal with Wade Elliott finding the head of McCann who put his effort just wide. At the other end a strike from Rory Delap kept Kiraly interested.
But it was Burnley substitute Joey Gudjonsson who came closest with two long-range efforts which were beaten away by Simonsen to keep the scores level.