He finished at 16-under-par 268, one stroke ahead of six players, including former champion Kevin Na (67), whose 15-foot birdie chance at the last shaved the hole, and overnight leader Brett Stegmaier (69).
Stegmaier also missed a good birdie opportunity at the last.
Kaufman, a 23-year-old from Alabama playing in just his fifth PGA Tour event, collected $1.152 million, along with an invitation to next April's Masters.
It was the mention of the latter, rather than the money, that reduced Smylie almost to tears.
"I can’t put it into words," he told Golf Channel, his voice cracking with emotion.
"I’ve been hitting it so good the last two days. I just wanted to give myself a chance and post a number.
"I dodged a lot of bullets coming down the stretch. Just thankful to get the W."
The long wait to see whether his score would hold up had been way more stressful than his round.
"I feel like I’ve been watching an LSU (Louisiana State University) football game," he said, referring to his alma mater.
Kaufman, whose middle name is Smylie -- his first name is Carter -- continues a trend of young tour winners. The past six events have been won by players 27 or younger.
Na, meanwhile, could only lament another near-miss, after losing a playoff in the season-opener last week.
He seemed poised for another playoff until he bogeyed the par-three 17th, after a poor chip that he was trying to hole from 25 feet.
"I felt it was a good position to chip it in. The lie was almost sitting up too good," said Na, who posted his eighth runner-up finish on tour. His lone tour victory came in Las Vegas four years ago.
Tour rookie Stegmaier also rued what might have been, having shared the lead after 36 holes and held it outright after 54.
"Can’t be too disappointed but certainly now it stings a little bit," he said.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Larry Fine / Ian Ransom)
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