Emlyn Aubrey and Nolan Henke finished five shots back at 3-under 277 in a tie for fourth.
Williamson, who had a one-shot lead after the second round, got off to a quick start under windy conditions at Crestview Country Club and secured the victory with a key par save from five feet on the final green.
'I just aimed it at the right edge,' said Williamson, who pocketed $76,500 for the win, his first on the Buy.Com Tour. 'It was nice watching it those last six inches because I knew it was going in. You can't describe that feeling. It's something you can't practice. You only get to experience it a few times. It's an amazing feeling and everybody should have that opportunity.
Williamson opened with two birdies over his first four holes but dropped a shot at the at the par-4 sixth. It was on the back nine that Williamson grabbed a share of the lead when he birdied 11 and 13 to match Cotner at minus 7.
The 30-year-old took the lead outright at the par-4 16th. He knocked a wedge inside two feet of the hole and drained the short birdie putt to stand alone atop the leaderboard, but was unaware of his position.
'I've been working with a sports psychologist and we've talked about the leaderboards,' said Williamson. 'He said if you're going to look at it, look at it. Memorize it. Either that or don't look at all. Today I had no concern to look at it. The golf course was tough enough.'
Cotner was in control of his round until a double-bogey at the 13th dropped him to minus 5. Cotner responded well with a birdie at 14 but was still trying to dig out of a hole.
After Klauk completed a bogey-free round of 65 to enter the clubhouse at 7-under, Cotner needed an eagle at the par-4 18th to tie Williamson for the lead.
'I kept saying 203, 3-iron, 203, 3-iron. I tried to treat it just like a putt,' said Cotner. 'I was thinking 'make it.''
Cotner sent his approach off the back of the green before he chipped in for birdie to join Klauk in a tie for second.
Arron Oberholser, Chip Beck and Tom Carter tied for sixth place at 2-under-par 278. Patrick Moore, still searching for his third win of the season and an automatic promotion to the PGA Tour, finished alongside Jimmy Walker and Jeff Freeman at minus 1.
Full-field scores from Wichita Open