Badou Ndiaye gave Stoke an 11th-minute lead, converting Mame Biram Diouf's pass with the help of a deflection.
But Ashley Barnes equalised on 62 minutes with his sixth goal in his last eight Premier League matches. He converted a loose ball after Jack Butland had saved from James Tarkowski.
Stoke almost grabbed a much-needed victory two minutes from time, but Stephen Ireland's shot hit a post.
They move to 29 points, four behind 17th-placed Swansea City. Burnley remain seventh, with 53 points.
Stoke City: 28 April v Liverpool (A)
Burnley: 28 April v Brighton (H)