The 51-year-old Dawson shot a 3-under 69 to finish at 13-under 203 in the first-year event at Tucson National, the longtime home of the PGA Tour's defunct Tucson Open.
Dawson won in his 21st start on the 50-and-over tour. He's winless in 412 PGA Tour starts and has one victory in 161 events on the Web.com Tour.
Dawson bogeyed the par-4 15th to fall into a tie with Bart Bryant at 12 under. On the 16th, Dawson's birdie putt barely tumbled in, and Bryant made a bogey after driving into a bunker.
Bryant had a 70 to finish second for the second straight event. He lost a playoff to Lee Janzen last month in Naples, Florida.
Paducah's Russ Cochran shot a final round 68 and tied for sixth at 8 under. Lone Oak alum Kenny Perry finished tied for 21st after a final round 70.
