Burnley took a first half through Samuel Bastien - before Jordan Shipley's superb lobbed effort brought Salop level just after the break.
Ne Jai Tucker put the Clarets back in front before Bobby Thomas scrambled home a third late in the game.
'Impressive from Salop': Lewis Cox and Jonny Drury on Shrewsbury's pre-season defeat to Burnley - WATCH
Lewis Cox and Jonny Drury discuss Salop's 3-1 pre-season loss to Burnley.
