Four strokes off the pace heading into a weather-interrupted final round that ended in fading light, Blixt fired a three-under-par 67 in rain-softened conditions on The Greenbrier's Old White Course.
The 29-year-old Swede held his nerve over a pressure-packed closing stretch, mixing four birdies with two bogeys over the last 10 holes to post a 13-under total of 267.
American Wagner, two ahead overnight in his bid for a fourth US Tour victory, dropped three shots after the turn as he struggled for accuracy off the tee on the way to a 73 and a four-way tie for second place.
Also finishing at 11-under were Wagner's compatriot and playing partner Jimmy Walker (71), and Australians Steven Bowditch (68) and Matt Jones (68).
Blixt, who had missed eight cuts in 16 starts on the 2013 PGA Tour before this week with a best finish of joint 11th at the Crowne Plaza Invitational in May, choked back the tears as he reflected on his come-from-behind win.
"This year has been kind of a bad year for me so to pull it off, I can't believe it," the emotional Swede, who earned an automatic place at next year's Masters with his triumph, told Golf Channel.
"I am really happy. Just to be able to play Augusta (National) ... so many dreams come true.
"It's just one week and the whole year kind of turns around," added Blixt, who clinched his maiden US Tour title by one shot at last year's Frys.com Open.
The final round was interrupted by a weather delay of just over three hours as thunder rumbled and lightning cracked overhead and a Monday finish appeared to be on the cards when the action finally resumed in the late afternoon.
Wagner eventually teed off in the last pairing under leaden skies and light drizzle and he three-putted for bogey at the par-four second for his overnight lead to be cut to one at 13 under.
However, Walker followed suit when he three-putted from well below the hole at the par-three third to hand Wagner a two-stroke advantage.
Though Walker rebounded with a birdie at the par-four fifth, where he struck a superb approach to six feet, Wagner responded with a curling 15-footer to birdie the sixth and regain his two-shot lead at 14-under.
Blixt briefly trimmed Wagner's advantage to one with birdies at the fifth, ninth and 10th but the Swede slid back with a bogey at the par-four 11th after missing the green to the right with his approach.
Wagner then bogeyed the 11th after hitting a poor chip from greenside rough and was caught in a two-way tie at the top at 13-under when Blixt knocked in a five-footer to birdie the par-five 12th.
The Swede also succumbed to the pressure over the closing stretch when he bogeyed the par-four 13th after finding the left rough off the tee.
Moments later, Wagner faltered at the same hole, a three-putt there dropping him back into a tie for the lead with Blixt at 12-under.
Blixt seized the outright lead for the first time by sinking a nine-foot birdie putt at the 16th and soon after found himself two strokes in front when Wagner bogeyed the short 15th after missing green to left off the tee.
As twilight fast approached, Blixt narrowly missed a seven-foot birdie putt at the 17th, then safely two-putted from long range at the par-three 18th to remain at 13-under, two ahead of the chasing pack.
Striving for late birdies, Wagner and Walker each parred the last three holes to ensure that Blixt would celebrate a second victory on the US Tour.
"I am so happy I pulled it off," said the Swede. "It was a little bit 'iffy' today but I pulled out some really good shots and had some short birdie putts that I could make. It's awesome."