Mark Hensby, who held the lead after 54 holes, carded a 69 to finish one shot back at 18-under-par 266 along with Mike Brisky. Wil Collins and Blaine McCallister followed at 17-under-par 267.
'This is what I've worked so hard for all my life,' said Klauk. 'Getting my first win is awesome. Knowing that you can do it changes everything.'
Klauk was two shots back to start the day at Crestview Country Club and jumped out of the gate with a birdie at the par-4 first. Klauk then added birdies at three and five to make the turn at 17-under before stumbling with a bogey at the 10th.
The tournament swung in Klauk's favor down the stretch and the 25-year-old picked up birdies at the 14th and the 16th. At the last, Klauk sent his second shot within 12 feet of the hole and two-putted for the decisive birdie.
'I really wanted this tournament especially after finishing second here last year,' said Klauk, who earns $85,500 for the win.
Hensby, who won this year's Henrico Country Open, was in control early with back-to-back birdies starting at the par-four first.
The 32-year-old soon found trouble, however, and tallied two consecutive birdies from the seventh to find himself trailing after the first nine.
Hensby's problems continued on the inward half with a bogey at the 10th but the Australian recovered with a birdie at the very next hole.
Hensby tried to pull off a late rally with a birdie at the 15th but fell short despite a birdie at the last.
'I birdied the first but I was making my victory speech before we were done,' said Hensby. 'I'm proud of how I finished. You just try to give yourself chances to win golf tournaments.'
Ryan Palmer fired an 8-under 63 to finish three shots behind Klauk at 16-under-par 268. Palmer was joined by Brad Ott, Omar Uresti and Tag Ridings in a tie for sixth.
Hunter Haas, Andre Stolz, Richard Barcelo, Jason Schultz, Ken Duke, Nick Cassini and Bob Friend were one shot further back at 15-under-par 269.