With brother Patrick serving as caddie, Gotterup captured the top prize of $1.584 million from the $8.8 million tournament as he heads for Europe to defend his title next week at the Scottish Open.
"To come out here and have Patrick out with me — just so awesome," Gotterup said, breaking down in tears. "Just a great week.”
"He just kept me in it all week. We were joking and having a good time. Just a fun week."
Gotterup took his fifth career PGA triumph and third tour victory of the year after winning January's Sony Open in Hawaii and February's Phoenix Open.
World No. 14 Gotterup made nine birdies to shoot the low round of the week but was still deadlocked for the lead with fellow American Kohles as his rival stood in the 18th fairway.
Kohles, who was chasing his first PGA Tour title in his 120th tour start, hooked his approach left and into a water hazard, then missed a 45-foot par putt to give Gotterup the victory.
Kohles, ranked 169th in the world, then missed a bogey putt from inside four feet before making a double bogey at 18 and finish two behind Gotterup and one adrift of runner-up Max Homa in a share of third with countrymen Lucas Glover and Lee Hodges.
"I was a little in between. I hit an 8-iron and thought 9 was going to be too short," Kohles said.
"I was just trying to hit a three-quarter punch shot. Just tugged it a little and ended up in the water.”