Stadler, the 33-year-old son of PGA Tour winner Craig Stadler, closed with 3-under-par 68 for a one-stroke victory over Watson and Canadian Graham DeLaet.
Stadler won in his 239th PGA Tour start, earning a spot in the Masters Tournament — a tournament his father won in 1982. The Stadlers are the ninth father-son winners in tour history.
Stadler finished at 16-under 268 at TPC Scottsdale. Raised in Colorado, he played in Denver Broncos colors, wearing an orange shirt and blue pants and hat.
Watson shot 71, and DeLaet had 65.
Augusta native Charles Howell shot 65 and tied for sixth at 271. Former Augusta State standout Patrick Reed had 72 and tied for 19th at 277. Former Louisville, Ga., resident Brian Gay shot 74 and tied for 61st at 285.