Spittle downed Jeff Sluman on the extra hole and captured his first Champions Tour title after birdying three straight holes down the stretch. He ended regulation with a 4-under-par 67, joining Sluman at 12-under 201.
Spittle won on the par-three 18th at the Oak Hills course in San Antonio after Sluman couldn't match his par.
Sluman had forced an extra hole thanks to back-to-back birdies on 15 and 16, also ending the third round with a 67.
Larry Nelson, meanwhile, failed in his bid to become the oldest winner in the senior tour's history. The 63-year-old came in with a 1-shot lead but stumbled to a 70.
He finished in third place with John Cook (68) and Taiwan's Chien Soon Lu (69) at 11-under 202.