The American, chasing his first PGA title, had eight birdies in a bogey-free round to stand on 16-under 197 after 54 holes at Quail Hollow in Charlotte, North Carolina.
"I felt like I was really mentally strong," Clark said. "It's a high-pressure, tough golf course and early on guys were making birdies.
"I just stayed really patient and I was as they say kind of in the zone and really focused out there. Felt good about it."
US playing partner Schauffele, the reigning Olympic champion, went four-under over the last five holes to shoot 64 and grab second on 199.
"Monkey see, monkey do is definitely a thing that happens out here," said Schauffele. "Fortunately it was the guy next to me (playing well)."
Australia's Adam Scott, the 2013 Masters champion and a former world number one, shot 67 and shared third on 202 at the $20 million event with England's Tyrrell Hatton, who had 68.
World number 80 Clark, seeking his first PGA title, has had three top-six finishes in his past five starts.
His only other top-five showing came at the 2020 Bermuda Championship, when he lost a playoff to Brian Gay.
Clark attributes some of this year's success to work on his mental approach.
"I meditate every day if I can, read a lot of books and then I've been setting mental goals versus outcome goals," he said.
"I'm trying to get myself in the right mindset for the day. If I can do that I'm hoping the scores take care of itself and thus far it has."
Clark reached the first 17 greens in regulation and was just into the fringe at the 18th.
"I missed the green," he said. "I'll take anywhere on green grass. I'm happy it wasn't wet."
He sank a 22-foot birdie putt at the second hole and reeled off three birdies in a row starting with a putt from just outside six feet at the par-three sixth. He then reached the green in two at the par-five seventh to set up a tap-in birdie and sank a 10-foot birdie putt at the eighth.
He made a seven-foot birdie putt at the par-five 10th and an 11-foot birdie putt at the par-three 13th, then dropped in a seven-footer for birdie at 14 and made a four-footer to birdie the par-five 15th.
"It's a tough golf course but he's making it look pretty easy," US rival Max Homa said of Clark. "I imagine he's quite confident."
Schauffele, seeking his eighth career PGA title and first of the year, has seven top-10 finishes this season, including his past four starts.
Schauffele reeled off four birdies in a row from the par-five seventh to par-five 10th holes and answered a bogey at the 12th with a birdie at 14, a 26-foot eagle putt at the par-five 15th and a 12-foot birdie putt at 16 to pull within two of Clark.
He could have matched Rory McIlroy's 2010 effort with six threes to close his round but missed an 11-foot birdie putt at 18.
"If you hit really good chips and good putts, you get rewarded," said Schauffele. "You've got to be in the fairway."
World number 18 Hatton, a six-time winner on the European Tour, captured his only PGA title at the 2020 Arnold Palmer Invitational.
World number 41 Scott seeks a 15th PGA victory and his first since 2020 at Riviera.
