Pettersson birdied three of the final four holes to reach 21-under 259 at the Sedgefield course. He made bogey on 18.
He not only earned his third PGA Tour win but he posted a tournament record low score.
American Scott McCarron, who took the lead after the 11th hole, shot 68 to claim second place at 19-under, with Rich Beem (63) another two strokes behind in third place.
Pettersson started the final round with a two-shot lead, but he was in danger of defeat after missing short putts to bogey the 10th and 11th holes.
But cheered on by a supportive gallery in the city where he went to high school, he outplayed McCarron down the stretch.
“I’m thrilled. This is home for me,” he said after recording the low score that dates back to 1938.
Pettersson is the third Swede to win on the PGA Tour this year, and the second to prevail in Greensboro, following 1999 champion Jesper Parnevik.
And though Pettersson remains a long shot to earn an automatic Ryder Cup berth on the European side, he must be one of the names Nick Faldo will consider when he makes his two captain’s picks in two weeks.
Pettersson, who moved to Greensboro at the age of 15 when his father, a Volvo executive, received a job transfer, admits he feels more American than European, but that doesn’t mean he wants to sit out the Ryder cup.
“I’m Swedish, but I really feel American, to be honest with you,” he said.
“My heritage is European and I would love to play on Nick’s team. I’m going to be playing hard for Europe if I make that team.”