He shot Gretna in front after 25 minutes of an ill-tempered replay and bagged two more as Gretna took control of the second half.
Clyde's night went from bad to worse when they had defender Craig McKeown sent off for two yellow cards in the 77th minute.
By then Gretna were three goals up and there was no way back for their First Division opponents.
Grady got on the end of a quickly taken Steve Tosh free-kick to rifle home an angled shot after 25 minutes.
Clyde defender Eddie Malone hit the bar with a 25-yard drive 10 minutes before the break and Tosh cleared a Crain Bryson shot off Gretna's goalline as the visitors fought for an equaliser.
But two goals in three minutes killed off their comeback hopes, Kenny Deuchar scoring from close range after a Grady flick-on and Grady scoring with a 25-yard drive.
And the Gretna hot-shot added his third in the 81st minute with a low shot across Peter Cherrie.