Henley birdied the final hole of regulation for a 5-under 65 to match Staten at 10-under 270 on Dye's Valley Course at TPC Sawgrass. Staten finished with a 68, then had a double-bogey on the playoff hole.
Henley had five birdies in a front-nine 30, but opened the back nine with seven straight pars before bogeying the 17th to drop a stroke behind Staten.
"I pretty much went into 18 thinking I have to make birdie," Henley said.
Henley hit his approach to 15 feet and made the putt to get back to 10 under.
"I remember I was reading something about Jack Nicklaus in a magazine about making pressure putts," Henley said. "It said to believe in your line and make a confident stroke, and I did that right there. I just tried to put a confident stroke on it, had the right read, and it was really cool seeing it go in."
Henley earned $108,000 to jump from ninth to third on the money list with $365,366. The tournament was the final full-field event of the year. The top 60 on the money list qualified for the season-ending Web.com Tour Championship next week in McKinney, Texas. The final top 25 will earn 2013 PGA Tour cards.
Henley also won the Chiquita Classic last month in North Carolina, beating Patrick Cantlay and Morgan Hoffmann with a par on the first hole of a playoff. Last year while still a student at Georgia, Henley won the tour's Stadion Classic on his college course.
"Honestly, I'm just happy to be competing," the 23-year-old said. "I enjoy competing more than I do getting done and looking back on it. I just love feeling nervous, feeling the pressure and having to hit shots and I think that's helped me out."
Staten earned a spot in the finale, making $64,800 to go from 69th to 32nd on the money list with $141,521.
Ben Martin shot a 68 to finish third at 8 under. He jumped from 94th to 60th on the money list.
Aaron Watkins was 6 under after a 67, and Cantlay was another stroke back along with Kevin Foley and Wes Roach. Cantlay closed with a 72, Foley shot 67, and Roach had a 69. Foley also moved into the top 60, going from 66th to 54th.