Blixt carded a final-round three-under par 67 in the gloom to finish two clear of a group of four on 13-under for the tournament, which was delayed by three hours on Sunday by rain.
Playing one hole ahead, Blixt traded birdie with bogey at 12 and 13, but moved two clear when he holed a six-foot birdie putt at 16, leaving him a nervous wait in the clubhouse.
Wagner and Jimmy Walker both reached the 17th green needing a birdie-birdie finish to force a play-off, but were forced to settle for pars and Blixt’s title was assured.
“It has been a bad year for me but I just pulled it off,” said Blixt after his first top-10 finish of the year. “I can’t believe it. I’m just really happy.”
His victory means he has earned an invitation to next year’s US Masters.
“A dream come true,” he added. “I watched (the Masters) when I was a kid. I always wanted to play there. It’s a special place, almost like a religious experience to be there. To play there, I’ve just got no words for it.
“It’s so many dreams come true. It’s one week and the whole year turns around. It’s really special.”