Stuart Drummond put the Shrews ahead after just three minutes at Wembley when he headed home from Neil Ashton's cross.
Richard Walker's brace saw the Pirates ahead before the break, and Sammy Igoe made it 3-1 in second-half stoppage time.
He picked up the ball on the edge of his own area following a corner, ran the length of the pitch and passed the ball into an empty net as Shrews keeper Chris MacKenzie had gone up for the corner.