Pappas, the third-round leader, posted a two-under 69 in the final round to finish at 16-under-par 268. Wi shot a three-under 68 to come in one stroke behind at the TPC Wakefield Plantation.
Wi took a one-shot lead into the final two holes, but Pappas matched him at 15-under par when he knocked his wedge to three feet at the 17th. Pappas drained the birdie putt to tie the pair with one hole to play.
'I was conscious about not worrying about the leaderboard,' said Pappas. 'Walking off 17 I wanted to know where Charlie and I stood relative to the guys who had finished.'
At the par-five 18th, Pappas drained a 25-foot birdie putt, but Wi, who won this year's Malaysian Open on the European Tour, hit a hazard with his third, but his ball came back to 20 feet. Wi's putt never fell, giving Pappas his first victory on the Nationwide Tour.
'I've been dedicated to this, stubbornly, for two months,' said Pappas, who collected $81,000 for the victory. 'I've worked hard and my whole preparation has been around winning.'
'I got very lucky to be on the green and have a birdie putt at it,' admitted Wi. 'It was a double-breaker. Those are tough. Sometimes they go in and sometimes they don't.'
Tripp Isenhour, a two-time winner this season on the Nationwide Tour, carded a four-under 67 on Sunday to share third place with Michael Putnam, who posted a three-under 68 in the final round. The pair finished at 12-under-par 272.
Pappas hit an errant pitching-wedge at the 10th and made bogey. That dropped Wi and Pappas into a tie for the lead, but Wi assumed the top spot on the leaderboard with a birdie at the 12th.
Pappas' closing performance sealed the victory and moved him to sixth on the Nationwide Tour money list.
Jim Rutledge (65), Brad Adamonis (65), Michael Sim (65), Bob Heintz (66), Scott Gutschewski (68), Boo Weekley (68), Neal Lancaster (68), Brendon de Jonge (68) and Brad Klapprott (69) shared fifth place at 11-under-par 273.