The 25-year-old Tway, the son of Champions Tour player Bob Tway, closed with a 7-under 64 at Hillcrest Country Club to match Levin at a tournament-record 23-under 261.
"My hands were shaking a little bit," Tway said about his winning putt. "It was on the same line I had in regulation and I just wanted to make sure I got it to the hole."
Levin finished with a 63. Making his second start since hand surgery last fall, he missed a 10-foot birdie try in the playoff.
Tway earned $139,500 to jump from 39th to sixth on the money list with $219,794, wrapping up a spot next season on the PGA Tour.
"This means a lot because I've struggled since turning pro," the former Oklahoma State player said. "This really hasn't sunk in yet. I've always wanted to play on the PGA Tour since I was a little kid."
Michael Putnam, a two-time winner this year who tops the money list with $430,684, had a 63 to tie for third with Bronson La'Cassie and third-round leader Philip Pettitt at 22 under. La'Cassie had a 65, and Pettitt shot 67.
Russell Knox, the Scot who shot a 59 on Friday to match the tour record, finished with a 69 to tie for 12th at 19 under.