"This is what I play for," Blixt said. "I play to win. It just confirms that if you do the right things, that you work hard, dreams can come true."
Among the perks for his victory are a spot in next year's Masters.
Blixt also will move to around No. 50 in the next world ranking, which is used as the alternate list to fill the field for this month's British Open. That would make him the top alternate in a year when about eight players from the list will get into the Open at Muirfield.
He overcame a four-shot deficit at the start of the final round and finished at 13-under 267. Third-round leader Johnson Wagner (73), Australians Steven Bowditch (68) and Matt Jones (68), and Jimmy Walker (71) tied for second at 11 under.
Former BYU golfer Daniel Summerhays (67) finished in an eight-way tie for ninth place at 8-under 272.
Blixt went from a tie to a two-shot lead when he made a 9-foot birdie putt on No. 16 to move to 13 under. No other player made a birdie after that. Wagner bogeyed the par-3 15th moments later to fall to 11 under alongside Bowditch and Walker.
Blixt also won the Frys.com Open last year as a tour rookie. But entering the Greenbrier Classic, he hadn't had a top-10 finish this season.
In Saint-Quentin-En-Yvelines, France, Graeme McDowell of Northern Ireland won the French Open, shooting a 4-under 67 in the final round to capture his ninth European Tour title by four strokes. McDowell finished at 9-under 275. Richard Sterne of South Africa (71) was second.