Cook ended with a 21-under 195, three shots better than second-round leader Chien Soon Lu.
The 53-year-old cruised to a new tournament scoring record, besting the Club de Golf Fontainebleau record of 199 set last year by Larry Mize.
Lu closed with a 2-under 70, finishing alone in second at minus-18.
Holding third at minus-17 was Joey Sindelar, who carded a 4-under 68.
Mize (67) ended with a share of seventh place at minus-15.