Shelley shot a bogey-free 8-under 62 to leap 12 spots on the leaderboard and force a playoff with second and third-round leader Jack Buchanan of Australia.
Buchanan struggled, shooting a 1-over 71 but was still able to get in the playoff at 13-under with Shelley.
In the playoff, both players made par on the first hole, and then on the par-5 second hole, Buchanan missed the green and made par while Shelley was on the green in two shots and had a stress-free two-putt to win the championship.
Shelley added, "I didn't really know what I was at score-wise until I looked on the 18th green and saw that I was in contention."
The 62 tied the competitive course record and the lowest tournament round of Shelley's career.
"I actually started the round off slow by making par on the getable par-5, and then the birdies came afterward," Shelley said. "I wanted to play consistently throughout the day and give myself good looks all day."
After 72 holes and four days of golf, Shelley still had plenty of energy heading into the extra holes against Buchanan.
"I felt good during the playoff," Shelley said. "I did have a lot of adrenaline going, which pumped me up but overall, I felt like I had great energy to keep going."
Chuan-Tai Lin of Taiwan, Neal Shipley of Pittsburgh, Pa., and Jeffrey Guan of Australia all finished T3 at 11-under par.
Omar Morales of Mexico also had a phenomenal day, shooting 6-under 64 to vault 18 spots up the leaderboard and finishing T6.
Shelley knows how important this win is, with it being an Elite Amateur Series event and a talented field.
"It means a lot to me and my confidence," Shelley said about the win. "Especially this last round. It made me realize that a tournament is never over until it is over. I think this win has my confidence high, and I am able to compete at high levels in any tournament."