On a day unlike any other in his career, world number one Scheffler was arrested on four counts, including second-degree assault of a police officer, after what he said was a "big misunderstanding" as he tried to enter Valhalla Golf Club.
Scheffler, seeking his fifth win in six starts and playing in a steady rain that greeted the early starters, carded a five-under-par 66 that left him in a share of fourth place at nine under and chasing Schauffele (68) at the year's second major.
"I definitely never imagined ever going to jail, and I definitely never imagined going to jail the morning before one of my tee times," said Scheffler.
"But yeah, like I said, I was grateful to be able to go out there and compete... It was definitely a nice round of golf."
Overnight leader Schauffele, playing in his 28th major and seeking a breakthrough win, went out with the late starters, and the only blemish on his scorecard came at the par-three 11th where he three-putted for bogey.
"When you haven't won a golf tournament in a few years, you have to be pretty resilient," said Schauffele. "I'm just patient and trying to play the best golf I can and stay out of my own way."
Twice major champion Collin Morikawa (65) was a shot back of Schauffele, while Sahith Theegala (67) was a further shot adrift. Play was eventually suspended due to darkness, but none of the 17 players left on the course could catch Schauffele.
LIV Golf's Bryson DeChambeau (65) was among those in a share of fourth place.
Despite the chaos, Scheffler looked calm throughout a round that he began with a birdie at the par-five 10th hole, where his third shot from 97 yards settled three feet from the hole.
The Masters champion went bogey-birdie over his next two holes, carded three birdies over a five-hole stretch around the turn before nearly holing out for birdie at the par-four fifth. Scheffler added another late birdie.
Lone bogey
Morikawa, who started on the back nine, caught fire at the par-four fourth, his 13th hole of the day, where he made the first of five consecutive birdies - the longest streak of his major championship career - to grab control.
The twice major champion made his lone bogey at the final hole, which dropped him to 11 under and one shot shy of the PGA Championship record for lowest score in relation to par through 36 holes set by Brooks Koepka in 2019.
"Just kept it in front of myself, and look, I've been putting great so far since Augusta, so it's nice to just kind of keep that trend going," said Morikawa.
"Hit a few good close shots, few wedge shots, take advantage of the short holes, the par-5s and for the most part didn't really make any big errors, other than the last hole, just that approach shot."
Defending champion Koepka, looking to become the event's first repeat winner since he successfully defended the title in 2019, was five shots off the lead after a three-under-par 68.
Northern Irishman Rory McIlroy will have plenty of work to do if he hopes to earn his first major in a decade, as he was seven strokes back of Schauffele after an even-par 71.
Tiger Woods missed the cut after a horrendous start to his round, during which he had two triple-bogeys and a bogey through four holes en route to a six-over-par 77 that left him at seven over on the week and eight shots outside the cut line.
"Just kept making mistakes and things you can't do, not just in tournaments but in majors especially. And I just kept making them," said Woods. "I hung around for most of the day but unfortunately the damage was done early."
The start of the second round was delayed 80 minutes after a worker with one of the tournament vendors was killed after being struck by a shuttle bus outside Valhalla Golf Club.
