Playing with his brother Patrick on the bag, Gotterup finished on 20-under 264 to claim his third PGA Tour title of the season and fifth career PGA Tour victory, before heading to Scotland to defend his title at next week's Scottish Open.
"To come out here and have Patrick out with me - just so awesome," Gotterup said tearfully. "Just a great week.
"He just kept me in it all week. We were joking and having a good time. Just a fun week."
The world No. 14 produced the lowest round of the tournament, making nine birdies to charge into contention after starting the final day five strokes off the lead. He briefly moved into a share of first before a birdie at the par-five 17th took him to 20 under.
Kohles reached the 18th fairway tied for the lead. Chasing his maiden PGA Tour title in his 120th start, Kohles hooked his approach into the water, then failed to hole lengthy par and short bogey putts, finishing with a double bogey that left him tied for third on 18 under alongside Lucas Glover and Lee Hodges, two shots behind Gotterup.
"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.
"Tough way to finish, especially how I played all day. I'm proud of the way I played. Sucks to just have that happen on the last hole, but learned a lot about myself... and it's only going to make me better going forward."