The 26-year-old American stood on 13-under par 197 after 54 holes at Colonial Country Club in Fort Worth, Texas, with five rivals deadlocked behind him on 198.
South Africa’s Branden Grace and Americans Gary Woodland, Justin Thomas, Collin Morikawa and Jordan Spieth were one adrift with Americans Daniel Berger and Harold Varner on 199.
“All of us, everyone, it’s like six guys are tied for the lead,” said world number 12 Schauffele, who is bidding for his fifth PGA Tour title but first since January 2019.
“Birdies are important but bogeys are bad. It’s really unique because everybody is so bunched.”
World number one Rory McIlroy of Northern Ireland shot 69 to join a pack on 200 that included England’s Justin Rose, Mexico’s Abraham Ancer, Canadian Corey Conners and Americans Patrick Reed and Bryson DeChambeau.
The tournament marks the return of the US golf season after a 91-day layoff since early March due to the coronavirus pandemic and is being played without spectators.
“It really was quiet out here,” said Schauffele. “I prefer fans.”
Schauffele has made 16 birdies and only three bogeys through the first three rounds.
“I was playing really well at home. I was making a ton of birdies,” Schauffele said. “I don’t see why it should change out here.”
Schauffele, who shared second behind Tiger Woods at last year’s Masters, credited his strong start from the long break to playing practice rounds with Charley Hoffman and Phil Mickelson during the layoff.
“It knocked off a lot of the rust that was there during quarantine,” he said. “I have to attribute it to that.”
Schauffele opened with a tap-in birdie but missed the green and a six-foot putt to bogey the par-3 fourth. He answered with another birdie at the par-4 seventh and tap-in birdies at 10 and the par-5 11th.
A 17-foot birdie putt at the 15th was wasted when he missed the green at the par-3 16th and made bogey, but his closing birdie gave him a nose ahead of the pack entering the last round.
‘Kind of a weird day’
Thomas also fired a 66 despite struggling much of the day to find a rhythm.
“It was kind of a weird day,” he said. “I definitely didn’t have my best stuff. Hit a lot of my best drives that bounced into the rough.
“I wasn’t quite sharp enough to get everything going with my approaches and putts so I’m glad to get to four-under.”
Woodland and Grace also shot 66s with Morikawa firing a 67 and Spieth a 68.
“Happy with my game now and the way I played,” Woodland said. “The key around here is put it in the fairway and keep moving forward.”
Varner, trying to become only the eighth African-American winner on the PGA Tour, led after 36 holes but fell two back with a third-round 70.
McIlroy, a top-five finisher in his past seven events worldwide, opened with a tap-in birdie but made bogeys at seven and eight. Birdies at the 11th and a 23-foot birdie putt at 14 only left him on 69 and three back.
Rose had six birdies but a double bogey at the par-4 fifth and bogeys at 16 and 18 also put him three shots off the pace.
“It has been a mixed bag for me. It has been exciting,” Rose said. “In with a chance tomorrow. Going to have to attack. It’s a great leaderboard.”