After sinking a clutch six-foot par putt at the final hole of regulation to force the playoff, Wiesberger clinched victory at the same par-four 18th with another par at the Renaissance Club.
Frenchman Hebert, without a European Tour victory, came close to pulling off a stunning upset when he surged from seven strokes behind in the final round, shooting a 9-under-par 62.
But his nerves betrayed him in the playoff as he three-putted twice, the second occasion proving the nail in the coffin.
Though he fell short, Hebert earned a consolation prize of a spot in the the Open Championship, which starts at Royal Portrush on Thursday.
Wiesberger was already exempt for the final major of the year.
The Austrian shot a closing 69 to match Hebert at 22-under 262, two strokes clear of Frenchman Romain Langasque.