A day after almost hitting Rory McIlroy with his drive at the reachable par-four 17th, Grillo became the sixth Argentine player to win on the American circuit, joining Roberto de Vicenzo, Jose Coceres, Angel Cabrera, Andres Romero and Fabian Gomez.
It is the second successive victory for the 23-year-old, who won the Web.com Tour Championship on the secondary circuit two weeks ago.
Grillo sank a 25-foot birdie at the final regulation hole to earn a spot in the playoff, but almost threw away the first event on the 2015-16 PGA Tour season when he lipped out his short putt that would have won it at the first extra hole.
The putt was eerily similar to one he missed at the 72nd hole that would have won the Puerto Rico Open in March, though Grillo claimed that this time he did not hit a bad putt.
"The difference is I hit this one good," he said in a greenside interview. "I don't know what happened (but) I stayed positive. This is awesome."
After Na made a mess of the second extra hole, Grillo had the luxury of two-putting for victory, but he needed only one, ensuring he would be remembered for more than being the guy who nearly hit McIlroy.
Earlier, Grillo (69) and Na (70) finished at 15-under-par 273, one stroke ahead of Americans Jason Bohn and Justin Thomas and South African Tyrone Van Aswegen.
Bohn held the sole lead with three holes left, but chunked a pitch shot at the par-five 16th and made bogey.
Van Aswegen barely made his tee time after waking up dizzy and going to hospital in an ambulance.
"I was not in good shape," he told Golf Channel. "They filled me with two bags of fluid and said I had severe dehydration and vertigo.
"If you go to the ER (emergency room), nothing's quick. I was trying to speed them along. I was still in the hospital bed an hour before the tee time. Thank goodness there was a slight fog delay."
Overnight leader Brendan Steele plunged out of contention with five bogeys in a six-hole stretch on the back nine. He shot 76 to tie for 17th on 10-under, one stroke better than McIlroy (69).
(Reporting by Andrew Both in Cary, North Carolina; Editing by Greg Stutchbury)
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