England's Dan Brown and South Korea's Im Sung-jae had shared the lead after early rounds of 66 at a scorched Royal Birkdale, before Suber moved top of the leaderboard.
Scheffler, bidding to become the first man since Padraig Harrington in 2008 to retain the title, carded a two-under 68 with DeChambeau a stroke better off.
Suber carded six birdies but his memorable moment came on the par-five 17th where a stunning second shot from next to a bunker to six feet resulted in a rare eagle.
He is the fourth player to post a round of 65 or lower on his Open debut.
"This was only my fifth day ever in Europe! So I'm definitely learning the links course," Suber said. "I settled a little more on the back nine, and felt more comfortable.
"The challenge is good. You can hit great shots that don't end up well, and bad shots that end up great. It's very cool where the ball can go."
Brown and Im took advantage of ideal scoring conditions early on in the seventh group out before the stiff breeze started kicking in off the Irish Sea.
Puffing regularly on cigarettes and making doubly sure to dispose of them carefully in the tinder-dry conditions, Brown made only eight pars in an up-and-down round, with seven birdies, including a superb up-and-down at the 17th.
"It's only Thursday so hopefully I'll be kicking around at the weekend in the later groups," Brown, who led after the first round at Royal Troon in 2024, said.
World number one Scheffler began as he finished last year at Royal Portrush -- making it look all too easy.
He rolled in four birdies in his opening six holes but a bogey at the seventh stunted his progress and then a few putts refused to drop. He missed a short par putt on the 17th after a wayward approach left his ball sunken down.
"I felt like I could have gotten a little bit more out of it, but yeah, if I continue to do what I did today with the ball-striking, I'll be in a good spot as the week goes on," Scheffler, who believed someone may have stepped on his errant ball at the 17th, told reporters.
"Golf is played over 72 holes, and I definitely liked what I saw today."
Playing partner DeChambeau looked in the mood to make an impression after missing the cut at the year's first three majors as he compiled a three-under 67, a bogey five at the 18th depriving him of a share of the clubhouse lead.
DeChambeau was in a large group on three under, including Belgium's Thomas Detry, Scotland's Robert MacIntyre, 2018 Open champion Francesco Molinari and American Alex Smalley.
Strong English contingent
After England's World Cup heartache against Argentina on the eve of the Open, home fans in the avalanche of ticket holders streaming across the Merseyside links course were hoping for some comfort from a strong English contingent.
No Englishman has won the Open since Nick Faldo at Muirfield in 1992 and one player looking to end that drought and win his first major is local hero Tommy Fleetwood.
The Ryder Cup player, who grew up close to Birkdale and used to sneak on to the course as a child, attracted huge galleries and plenty of encouragement across the dusty course and battled to a one-under 69.
Justin Rose endured a difficult day at the office though. The 45-year-old former US Open champion burst on to the scene as a 17-year-old amateur at Royal Birkdale in 1998, finishing fourth. But his hopes of finally winning the British Open were receding after an opening round 75.
High temperatures and a lack of rain have given Royal Birkdale a very different hue to its last appearance on the Open rota in 2017 when American Jordan Spieth won the Claret Jug.
Back then rain, wind and lush rough challenged the players but this time the course, remodelled since its last Open, is tinged with brown with fairways running fast.
"This is not the Birkdale I've ever seen before," 2009 Open champion Stewart Cink said after a four-over 74.