Burnley had looked to be coasting to victory after Ian Moore had given them a second minute lead with a close-range finish from a Robbie Blake free-kick.
Blake then made it even better for Burnley by converting a penalty after he himself had been fouled by Clint Hill.
Richard Chaplow then missed a great opportunity to put Burnley three up inside half an hour and how the home side were made to pay.
Akinbiyi scored from a yard following a corner from Dave Brammer before Burnley defender Michael Duff was harshly sent off for a dubious handball decision.
Akinbiyi equalised with a cool finish four minutes into the second half and Stoke really should have gone on to win an exciting game.
The fact that they didn't was largely to some poor finishing and some great goalkeeping from Danny Coyne.
Coyne made some great saves, none better than an excellent block from Gifton Noel-Williams.
Burnley might have snatched victory themselves when a shot from Blake was no more than a yard wide, but the home side deserved no more than a point.