Reigning Olympic champion Schauffele fired a seven-under-par 65 to stand on 17-under 199 through 54 holes at the $4.5 million (£3.53 million) US PGA Tour event on TPC Sawgrass in Ponte Vedra Beach, Florida.
"Just kind of made it work," Schauffele said. "I only hit two fairways on the back nine so feels good. It's nice to move up the leaderboard."
Schauffele began the day four adrift of leader Clark but was 6-for-6 getting up and down, sank a 58-foot birdie putt at 14, pulled ahead when Clark made bogey at the par-3 17th island hole and saved a clutch par at 18.
"When you're trying to compete out here, you have to have some things go your way, like that 58-footer," Schauffele said. "Got to clean up the small things."
Schauffele, whose most recent victory came at the 2022 Scottish Open, said winning his eighth career PGA title "would mean a lot to me".
"It has been a while since I've had the lead out here," Schauffele said. "Just going to try to enjoy myself and remind myself I'm good enough to win."
Clark struggled to a 70 after opening with back-to-back 65s.
"It was kind of my off day," Clark said. "I missed a couple putts early and a wedge on 17 but outside of that I thought I played pretty solid.
"I love where I'm at. I'm hoping I flip the script and have a Xander round tomorrow."
Reigning British Open champion Brian Harman was third on 201 after a sizzling 64 with England's Matt Fitzpatrick and American Maverick McNealy sharing fourth on 203.
World number one Scottie Scheffler, the defending champion battling a neck injury, shot 68 with birdies on the last three holes to stand on 204.
"Put up a good fight last couple days," Scheffler said. "Don't feel like I'm out of the tournament. Had a nice finish to keep myself in it."
Fifth-ranked Clark, who won his third career PGA title last month at Pebble Beach, battled down the back nine in an all-US fight for the lead.
They were deadlocked at the 14th when Schauffele sank his 58-foot stunner to seize the lead alone at 17-under.
Clark answered by reaching the green in two at the par-5 16th and tapping in for birdie while Schauffele found the right rough and a left greenside bunker but salvaged par.
At 17, Clark splashed into the water well short of the green before landing a second tee shot six feet from the hole and making his bogey putt while Schauffele's ball clung on the fringe and he two-putted for par to restore his one-stroke edge.
"I chunked it. It was user error," Clark said. "That was unfortunate. Making a birdie from there (for a bogey total on the hole) was huge and I think kept me in the tournament."
At 18, Schauffele was in the rough short of the green but blasted out inches from the hole and tapped in for par.
"That par on 18 was big for me," Schauffele said.
'Laser-locked in'
Clark said he needs better focus in the final round.
"I hope my mind is a little more focused," Clark said. "I was a little aloof, really just being present, not worrying about scoring. I'm hoping I'm really laser-locked in and can throw a great round at Xander."
Clark birdied the first and seventh holes while Schauffele birdied three of the first six holes.
Clark made a bogey at the par-3 eighth, missing a six-foot par putt, and Schauffele sank a birdie putt from just inside five feet at the par-5 ninth to pull within one at the turn.
Schauffele sank a birdie putt from just beyond 10 feet at the 12th to grab a share of the lead.
