The 34-year-old Na's only previous tour win came in Las Vegas in October 2011.
Overnight co-leader Harold Varner III had his worst showing of the tournament, mixing three birdies with three bogeys and a double bogey for a round of two-over 72 that extinguished his hopes of a first PGA Tour win.
Third-round co-leader Kelly Kraft carded an even-par 70 to claim second place at 266. Brandt Snedeker and Jason Kokrak tied for third at 13 under. Both shot 65. Sam Saunders was alone in fifth place at 12 under after a 67. He birdied six of the first 10 holes to open up a big lead, and he never looked back, cruising to a final-round 64, 19-under par for the tournament, which was good enough to win the event by five strokes.
Na had three dozen top-10 finishes since his first win and showed signs earlier this year that reaching the top again was still well within reach.
LPGA: In Oneida, Wisconsin, Sei Young Kim shot a 7-under 65 to become the first player in LPGA Tour history to go lower than 30 under in winning the Thornberry Creek LPGA Classic by nine shots.
On the 616-yard par-5 17th, Stallings had a birdie after hitting the green in 2 and two putting.
Anirban Lahiri of India, who shot a 61 in the second round, shot 71-76 on the weekend to end up tied for 39th at 5 under.
"Most importantly today I kept within myself", said Na, whose only blemish in his seven birdie round was a bogey on the par-four 11th.
At the U.S. Open last month, Mickelson intentionally violated a rule by hitting a moving ball on the green in the third round. Kim won the 2016 Founders Cup at 27 under, while Sorenstam won the 2001 Standard Register Ping at 27 under, the tournament where Sorenstam shot 59.
Kim also set the 72-hole scoring record at 257, finishing with three straight pars to break the mark by one shot.
He sank a five-foot birdie putt at the fourth and one twice as long at the fifth before dropping a 32-footer at the sixth. Fox failed to match the birdie, with his putt agonizingly lipping out, and Knox put his hands to his face.
Defending champion Xander Schauffele, who was one shot behind when the round started, bogeyed five of his first six holes.
"It feels fantastic", Na said.