Starting on the back nine, the PGA Tour rookie mixed six birdies with a bogey to reach five-under par with four holes to play.
Former US Open winner DeChambeau, one of 18 LIV Golf members in the 156-player field, carded a four-under-par 66 to move ahead of Scheffler and Canada's Conners on a day when the start of play was delayed by nearly two hours due to frost.
Keegan Bradley, who won the 2011 PGA Championship, was two shots off the pace with Norway's Viktor Hovland and New Zealand's Ryan Fox.
"It was a good day, five-under through the holes that I played was good," said Cole. "I played solid for the most part and got a couple of good breaks when I needed them, so it was a good day."
From scores to temperatures it was a day of highs and lows as a treacherous East Course bared its teeth with only 19 in the 156 player field getting under par.
An overnight frost delayed the start of play by nearly two hours, with golfers and spectators bundled up in wool hats, gloves and winter coats as action finally got underway.
By mid-morning the freezing temperatures and frost had given way to sunny skies before an evening chill arrived with 33 golfers still on the course.
DeChambeau, who missed last year's PGA Championship as he was recovering from surgery on his left hand, started on the back nine and reached the turn at one under. From there he went bogey-free and added three birdies.
Scheffler also began on the back nine and reached the turn at one under before adding birdies at the par-three fifth and the par-four eighth, where his approach shot settled three feet from the cup, en route to his first bogey-free round in a major.
"It was a grind today," said 2022 Masters winner Scheffler. "The golf course is very tough. And I think these are probably the easiest conditions we are going to have all week."
World number one Rahm, who won his second major title at last month's Masters, was brought back down to earth with an opening 76 that left him 10 shots off the early lead.
It marked the first time the top player in the rankings had carded a six over or higher at the PGA Championship since Greg Norman in 1987.
Rahm seemed unconcerned by the frost delay as he rolled in a 16-foot birdie putt at his opening hole, the par-four 10th.
The Spaniard, whose made cuts in each of the last 14 major championships is the longest current streak of its kind, was undone by an ugly six-hole stretch around the turn that included five bogeys.
"Couldn't find the fairway and the fairways that I missed cost me bogeys," said Rahm
World number three Rory McIlroy, who missed the cut at last month's Masters, got off to a slow start and reached the turn at three over but mostly steadied the ship after that and finished his day at one over.
"Messy," McIlroy said when asked about his round. "Didn't hit the ball well at all. Thought I did really well to shoot one over in the end ... but I am going to need to play a lot better than that if I want to feature in this tournament."
Brooks Koepka, who finished joint runner-up at the Masters, opened with a 72 while Jordan Spieth, making his seventh attempt at completing the coveted career Grand Slam of golf's four majors, shot a 73.
Six-time major winner Phil Mickelson, who also finished second at the Masters, went out with the late starters.
It marks Mickelson's return to the PGA Championship for the first time since 2021 when, aged 50, he defied the odds to become the oldest major winner in history.