The 26-year-old Tennessee native and former Vanderbilt player finished at 22-under 266 and earned $900,000.
Tim Petrovic (67) -- who was tied with Snedeker with two holes to play -- joined Jeff Overton (70) and Billy Mayfair (67) two strokes back.
Carl Pettersson (68) -- a North Carolina resident and a member of the tournament's board -- finished three strokes behind Snedeker, who joined Shigeki Maruyama (2003) and K.J. Choi (2005) as recent winners at 22 under at a Greensboro course dominated all week by high temperatures and low scores.
Snedeker and Petrovic were tied at 21 under with two holes to play and seemed headed to a playoff. Snedeker took the lead for good with a birdie on the par-3 No. 17, rolling in a 32-foot putt.
Petrovic, playing two groups behind him, landed his tee shot about 70 feet from the hole but missed his birdie attempt and tapped in from about 2 feet for par.
Snedeker then closed his round with an uneventful par on No. 18, while Petrovic sent his drive into the woods on the left side of the fairway and wound up finishing with a bogey.
Petrovic was denied his second career victory and first since 2005 when he won the Zurich Classic of New Orleans.
Snedeker was at 18 under before a late run of three consecutive birdies thrust him up the leaderboard, and that string was capped with one on the par-5 No. 15. What's more, he would have had an eagle had his 15-foot putt not drifted to the right of the hole. That was the second of two eagle opportunities for Snedeker, who settled for a birdie on the par-5 13th after his attempt rolled left.
In the end, those strokes wound up not mattering to Snedeker, whose previous best finish on the tour came in January when he was third at 12 under at the Buick Invitational.
Overton -- the 24-year-old former Indiana player who led after the second and third rounds and entered with a three-stroke lead -- fell off the pace after early trouble and was briefly overtaken before he rejoined the pack with a 44-foot birdie putt on the par-4 11th.