And after Shaun Newton and substitute Leon Clarke both hit the woodwork in extra time the game went down to a penalty lottery.
Carl Cort again missed when he hit the post and when Brian Jensen dived to his right to save from Seyi George Olofinjana, Burnley were through 4 - 2.
Earlier in the night Wolves went ahead on the stroke of half time when Newton pulled the ball back for the Ki-Hyeon Seol who slotted home from three yards out.
Five minutes after the break Robbie Blake who had hit the bar in the first half, passed the ball into the far corner from Mo Camara.