His 16-under 194 put him comfortably in front of Keegan Bradley (69) and Zack Sucher (71) at TPC River Highlands.
Sucher, the second-round leader, blew a five-stroke lead with a bogey, double-bogey, double-bogey start to the back nine.
Reavie, who tied for third in last week's U.S. Open, played the final nine holes in a course-record tying 28, 12 strokes better than Sucher.
"I just tried to stay patient and tried not to press," Reavie said after watching Sucher make four birdies on the front nine.
"So when I start making putts I think he started feeling it a little bit and started playing a little bit more aggressively than he normally would've."
Reavie, whose only PGA Tour win came at the 2008 RBC Canadian Open, put together four consecutive birdies to start the back nine, then added three more at the 15th, 17th and 18th holes.
He also birdied the eighth after his lone bogey at the sixth.
"Been feeling great with the putter for a while now," said Reavie, who also putted well in the U.S. Open.
Sucher was still optimistic despite the meltdown.
"The front nine was a lot of fun; back nine wasn't much," he said.
"I don't feel like I did that much wrong on the back (nine). The doubles on 11 and 12 weren't far off from being pretty good shots."
Sucher said he was not thrown off by Reavie's birdie run.
"It was more about me trying to get in with a good score," Sucher said.
Australian Jason Day (68) and Mexico's Roberto Diaz (67) shared fourth at nine-under.
Bryson DeChambeau (64) and Kevin Tway (66) were in a group of four at eight-under that also included England's Tommy Fleetwood (67) and Scotland's Martin Laird (68).
World number one Brooks Koepka stumbled home with a two-over 72, recording four birdies, four bogeys and a double that left him 15 strokes adrift of Reavie.
"I'm dead. I'm fried," said Koepka. "My body is starting to ache, too."
Defending champion Bubba Watson spiralled downward as well with six bogeys in a round of 73 that put him 14 shots behind at two-under for the tournament.
"I'm just trying to gear up and get ready for the next event," Watson said. "At some point I'm going to have a shot, and so I've got to stay ready and try to learn from this and keep moving on."
(Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Peter Rutherford)
