The 33-year-old Georgia native fired a 5-under 67 for a tournament total of 17-under-par 271 to finish one shot clear of Tim Petrovic, who shot 70, and third-round leader Steve Runge, who carded an even-par 72 at Le Triomphe Country Club.
'It's been a long time coming,' said Claxton, who collected $81,000 to jump from 51st to third on the season money list. 'I have been close a few times and I feel like my game has been getting better each year. It was a great day for me to come down the stretch, make the putts and finish the tournament the way I did.'
After sinking a 10-foot birdie putt at the 17th, Claxton knocked a 6-iron to within four feet at the 460-yard, par-4 closing hole to set up a final birdie. That moved him into a share of the lead with Petrovic, who made it to 17-under after matching birdies back at the 14th with playing partner Runge.
Petrovic bogeyed the 16th to drop back into second place at 16-under with Runge. The players had two holes remaining to at least force a playoff, but Runge missed a 15-foot birdie putt at the 17th and Petrovic's 12-footer was off the mark at 18.
'Two weeks in a row I placed second. I'm not going to complain,' said Petrovic, who also finished one shot out of first place at 16-under 272 in the Buy.Com Monterrey Open. 'I made some mistakes but I'm happy with the way I'm playing. I'm hanging in there not making too many mistakes so next time I get in position, hopefully I can pull off a victory.'
Petrovic's second runner-up showing in as many starts moved him into fourth place in earnings this year.
Petrovic, at 14-under and two back of Runge to start the day, took a one-shot lead with birdies at the first two holes and a Runge bogey at the first.
Petrovic bogeyed the fourth hole but made up for the lost shot with a two-putt for birdie at the par-5 5th. He was joined at the top of the leaderboard by Jeff Freeman, who surged to 16-under through eight holes on the strength of an opening eagle and three birdies.
Petrovic suffered a minor setback with a bogey at the eighth, but he returned to 16-under at the 10th after his approach left him with a foot for birdie. Runge fell to 2-over on the day with a bogey of his own at eight, then put himself in position to make a late run with the first of back-to-back birdies at the 13th.
Meanwhile, Claxton had made his way to 15-under with birdies from 20, eight, and 10 feet on the front nine, only to slip back a stroke after his tee shot found the water at the 12th. He rolled in a 12- footer to save par at the 13th, then two-putted from 30 feet for birdie at 14.
Freeman, who dropped out of contention with a double-bogey at the 13th, finished with a 69 for a share of 14-under 274 with Bob Gaus (65), Jody Bellflower (69), Jamie Rogers (69), Charles Raulerson (70) and Gene Sauers (70).
Monday qualifier David Lebeck, who fired a course-record 61 for the first-round lead, eagled the par-5 12th Sunday for a short-lived share of the top spot with Petrovic at 16-under. But Lebeck came back with a triple-bogey at 13 and finished in a four-way tie at 13-under par.
Michael Allen began the day in 60th place but turned in a final-round 63 that was made up of eight birdies, an eagle and a bogey at the last hole. He ended the event in joint 18th at 11-under.