'I really wasn't letting myself think about what a win would mean,' said Bryant, who earned $630,000 for the win. 'I was really focused on the present, and I don't know if it'll sink in until tonight or tomorrow what this win is going to mean for me.'
Patrick Sheehan closed with a 66 to take second place at 16-under-par 261. Dean Wilson, the second round leader, also posted a final-round, 4-under 66 to share third place at 15-under-par 265. He was joined there by Todd Fischer, who carded a closing 67.
Bryant opened the final round with a three-stroke cushion. After pars at the first two holes, he dropped in a birdie at the par-3 third at LaCantera.
The 41-year-old Bryant settled in with six straight pars to close his opening nine. He parred the 10th before draining his second birdie at the par-4 11th.
Bryant parred Nos. 12 and 13. He collected his third birdie at the par-5 14th. The New Mexico State graduate coasted to his first win as he parred his final four holes as he played the final 49 holes of the tournament without carding a bogey.
'My ball-striking has always been the thing that's carried me through. This week it was a little above average,' said Bryant. 'I hit the ball extremely well. Then I had that one day where I putted awfully well. I didn't miss anything Saturday.
'That seemed to be the thing that put me over the top. I had that one low round, and that's what I've been missing this year to have a real good tournament, and I finally got that.'
Bryant, along with his brother Brad, join three other sets of brothers to have won on the PGA Tour. The other winning brother combinations were Curt and Tom Byrum, Dave and Mike Hill, and Lionel and Jay Hebert.
Bart Bryant is playing the season on a major medical extension. He has had surgeries on both elbows and his shoulder since being an exempt player in 1992.
Sheehan opened with back-to-back birdies from the second. He moved to 4 under for his round with birdies at the eighth and 11th. Sheehan briefly moved to 17-under when he birdied the 14th. However, he faltered to his lone bogey at the par-4 16th.
'I played extremely well this week, every day,' Sheehan said. 'I think I had three bogeys for the week, and they all happened to be three putts, but when you can go a week with that little amount of mistakes, it should be a good week. I mean, I played fantastic.'
Jerry Kelly and Ted Purdy closed with rounds of 5-under 65 to finish at 14-under-par 266. They were joined in a tie for fifth place by Hunter Mahan (69), Tim Clark (68) and J.J. Henry (68).
Justin Leonard, J.L. Lewis, Scott Simpson and Heath Slocum were one stroke further back at minus-13. Tommy Armour III, the 2003 champion, finished in a tie for 41st at 6-under-par 274.