DeChambeau, who had missed the cut at each of the last three majors, carded a three-under 67 to sit two shots off the lead despite a closing bogey.
The two-time US Open champion said he was pleased with his game plan despite not finding enough fairways.
“I feel like I did a really good job today of being incredibly strategic and focused super hard on placing it in the right places,” DeChambeau said. “Besides 18, I placed the ball in some good areas. I just need to hit more fairways. Other than that, I feel like my strategy was nice today.”
World No 1 Scheffler, bidding to become the first player since Padraig Harrington to successfully defend the Claret Jug, opened with a two-under 68.
The American birdied four of his first six holes before two bogeys left him three shots off the pace.
McIlroy, meanwhile, struggled to a two-over 72 and trails the surprise leader by seven shots after an erratic display, though as one of the later starters, he had the worst of the conditions.
The Masters champion mixed four birdies with six bogeys, including dropped shots on both par-fives and a costly mistake at the 17th.
Despite his frustrating round, McIlroy believes he remains firmly in contention heading into Friday.
“Every time I made a stupid mistake, thankfully I made a birdie to keep myself in it,” he said.
“Not too far away. Hopefully we’ll get the better conditions tomorrow and maybe the greens are a little bit smoother in the morning. Go out there and shoot a good one and get myself right back in it for the weekend.”
