The 32-year-old American, the 2023 US Open champion, made eight pars before missing a three-foot par putt at nine to reach the turn at five-under, two strokes ahead of past US Open winners Dustin Johnson and Matt Fitzpatrick and Canada's Corey Conners.
Clark parred two holes Friday morning to complete a six-under par 64 opening round after a Thursday fog delay led to a darkness suspension that left 50 players on the course.
In his second round par streak, Clark found a greenside bunker at the sixth but sank a nine-foot par putt, then just missed the left edge of the hole on a 19-foot putt at the par-three seventh.
At nine, Clark lipped out on a 43-foot birdie putt then missed his comeback effort.
Consistency with wind, speedy greens and dense rough kept Clark at the top but also helped his top rivals.
Johnson, the 2020 Masters and 2016 US Open winner, birdied two of three morning holes to shoot 66, then made a bogey at the third and eight pars in round two.
England's Fitzpatrick, the 2022 US Open champion, parred his way through the front nine as well.
Conners joined the three-under par pack with a five-foot birdie putt at the first hole, his 10th of the second round.
American Gary Woodland, the 2019 US Open winner, began with a birdie to reach four-under but made bogeys on four of the next six holes to fall back.
Justin Thomas, a two-time winner of the PGA Championship, went three-under on the back nine to make the turn on two-under alongside fellow American Xander Schauffele, another two-time major winner.
Six-time major winner Rory McIlroy, the world number two from Northern Ireland, was set for a late start after opening on 69
Top-ranked Scottie Scheffler, who would complete a career Grand Slam with a victory this week, opened on 72 and goes off late as well.