Two strokes behind surprising leader Tyler Duncan entering the day at Silverado Resort and Spa, Steele birdied the par-5 16th and 18th holes -- holing a 3-footer on 18.
The 34-year-old Steele, from the Southern California mountain town of Idyllwild, finished at 14-under 273 for his third PGA Tour title. He also won the 2011 Valero Texas Open.
Finau, whose lone PGA Tour victory came in the 2016 Puerto Rico Open, moved into a tie for the lead with Steele at 14 under with a birdie on the par-4 13th. But he double-bogeyed the par-4 14th. After pars on 16 and 17, Finau had a 40-foot eagle putt on the 18th and settled for birdie and a 69.
Mickelson, who began the round four shots off the lead, birdied the 16th from 10 feet to move within one shot of Steele. But Mickelson, winless since the 2013 British Open, bogeyed the 17th before birdieing the 18th for a 70. It was Mickelson's 27th third-place finish in 27 PGA Tour seasons.
Hadley finished with a 73. He had a course-record 61 in the second round,
Duncan, a PGA Tour rookie who began the round with a one-stroke lead over Hadley, had five bogeys on the front nine and finished with a 75 to tie for fifth with Graham DeLaet at 11 under. DeLaet had a 72.
John Daly, the two-time major winner who won his first PGA Tour Champions title in May, closed with a 79 to tie for 72nd at 5 over.