Mediate was cruising but became vulnerable after carding bogeys on the 11th and 12th holes. He stayed in contention, however, by following with three straight pars.
He joined Bo Van Pelt in the lead with an 18-foot birdie putt on No. 16 and then holed out with his eagle on No. 17, ending with a round of 2-over-par 73, one shot better than Van Pelt (71) and Alex Prugh (69).
Mediate finished at 15-under 269, notching an eagle for the fourth straight day and taking his first title in eight years.
Prugh just missed a hole-in-one when his tee shot on the par-4 17th trickled to within 3 feet by the hole. If it had it gone in, it would have been only the second ace on a par-4 in PGA Tour history.
Rickie Fowler grabbed sole possession of fourth place en route to a 2-under 69 at minus-13 and Chris Tidland claimed fifth (69) one shot further back at minus-12.
Celebrity Families of 2014 [PHOTOS]