The 52-year-old Austin bogeyed the par-4 final hole after driving left into the water and ended up beating Jim Carter by a stroke on Omni Tucson National's Catalina Course.
Making his 28th start of the 50-and-over tour, Austin finished with a 7-under 65 for a 16-under 200 total. He was 5 under on the four par-5 holes with the eagle and three birdies.
Austin won the 2013 Sanderson Farms Championship at age 49 for the last of his four PGA Tour titles.
Playing in the group behind Austin, Carter birdied the 18th for a 68. The 54-year-old Carter, playing on a sponsor exemption, won the 2000 PGA Tour event at Tucson National for his lone title.
Bernhard Langer was third at 14 under after a 67. Playing alongside Austin, Langer drove into the right-side water on 18 and made a bogey. The German star was coming off a victory Feb. 14 in Naples, Florida.
Stephen Ames (69) and 2015 winner Marco Dawson (70) tied for fourth at 11 under. Scott Verplank, the second-round leader after his second straight 66, shot a 74 to drop into a tie for sixth at 10 under.