He hit 11 of 14 fairways and had 32 putts in 18 holes and no three-putts on the back nine.
This came one day after Blixt said he didn't know where the ball was going when he hit it with his driver.
"I had a really good range session last night," Blixt said. "I just stuck with that and whatever happened, happened. I pulled it off. I pulled off some really good shots and had some birdie putts that I could make."
Ted Potter Jr. was solid in defense of his 2012 Greenbrier Classic championship, but had just four birdies and a bogey to finish at 9 under. Potter secured his second top 10 finish of the season.
"I'm very happy to finish at 9 under," Potter said. "I just love the course, it's tree lined, it's tight and you've got to position yourself still in the fairways out there because of the bunkers out there, but I think it's a course that's fair to everybody."
Potter holds the distinction of finishing higher than any defending champion in the brief history of the Greenbrier Classic. Stuart Appleby followed his 2010 title by missing the cut in 2011 and Scott Stallings answered his title the next year by finishing tied for 56th.
He was relieved to hear the air horn to clear the course.
"I just snapped one in the bunker and had to chip one out and the wind was blowing," he said. "So having to get up and down from 130 yards, I didn't really want to hit that shot when the wind was blowing 20 at the time. I came back and made par so that was good."
But, it wasn't just Potter chasing Wagner. Walker, who was playing with Wagner, tied the three-time PGA Tour champion, as did Blixt. Matt Jones became the sixth player to reach 10 under in the tournament.
A birdie putt on No. 16 gave Blixt a two-stroke lead and Walker and Wagner did the rest. The only pairing following him couldn't get a birdie on No. 17, requiring an ace on the final hole.
With the victory, Blixt earns a $1.134 million share of the $6.3 million Greenbrier purse.
"Satisfaction, just knowing all the hard work has paid off," he said. "Very emotional too, I get to see my family very soon and very happy about that."