The tournament was played opposite the Wells Fargo Championship. a PGA Tour signature event in Charlotte, North Carolina.
Gotterup earned a spot in this week's PGA Championship, but not in the Masters or a guaranteed spot in the remaining two $US20 million signature events.
Four strokes ahead entering the round, Gotterup bogeyed the first two holes, then rebounded with a birdie-eagle-birdie burst on the next three.
"I felt good, like better than I thought I would feel coming out of the gates even though I made two bogeys," Gotterup said. "Kind of a crappy putt on the first hole and a really tough two-putt on the next. Then to bounce back the way I did, it's just kind of how I roll."
The 24-year-old former University of Oklahoma player won in his 27th tour start, finishing at 22-under 262.
"No matter what tournament or what my game feels like, I'm going to grind it out," Gotterup said. "That's kind of how I've always been."
Alistair Docherty (64) and Davis Thompson (68) tied for second. Ryan McCormick (64) was another stroke back tied fourth with Beau Hossler (67), Kevin Yu (67), Ryan Fox (67), Jorge Campillo (70) and Erik van Rooyen (70).
Blades Brown, the second 16-year-old in two weeks to make a cut, tied for 26th at 19 under after a 69. Last week, Kris Kim advanced to the weekend in the Byron Nelson.
Brown, from Nashville, Tennessee, is high school sophomore. His mother, Rhonda Blades Brown, played two seasons in the WNBA.
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