Despite a triple-bogey seven on the par-four ninth and two other bogeys, including one on the 18th, Scheffler retained a comfortable cushion at Muirfield Village after 54 holes.
The American is 10 under for the tournament, four strokes clear of Collin Morikawa, Austria's Sepp Straka and Canada's Adam Hadwin, who are all tied for second on six under.
Morikawa and Straka moved up Saturday's leaderboard after both carding four-under-par 68s, with first-round leader Hadwin staying in touch with a level-par 72 for a second consecutive round.
Newly crowned PGA Championship winner Xander Schauffele is six off the lead on four under after a third-round 71, tied for fifth with Sweden's Ludvig Aberg who finished with a 72.
But the chasing pack may be left ruing the failure to make inroads to Scheffler's overnight lead of three shots.
The leader started smoothly enough with back-to-back birdies on the second and third holes but found the water on par-five third to finish with a bogey six.
He regained that shot at the next hole with his third birdie of the day, but then imploded with a triple-bogey on the ninth.
After slashing his tee shot out of bounds to incur a penalty, Scheffler eventually reached the green but was left with a long putt for a double bogey, which duly rolled wide for his triple.
That left Scheffler at one over for the round at the turn, offering a chink of daylight for his pursuers, but in typical fashion, he regrouped and bagged three birdies down the stretch before a bogey five on 18 left him one under for the day.
Scheffler revealed afterwards that he had remained calm after his triple-bogey nightmare on the ninth.
"I was just frustrated," Scheffler revealed. "I feel like I hadn't hit many shots at all today off line and I had a triple on my card and I was all of a sudden one over par.
"I was definitely frustrated with the break, but overall I was like, I'm still swinging it really good, I didn't need to change anything, I just need to stay in the right frame of mind.
"I'm going to go out tomorrow and try and have a good round of golf, keep my head down and stay in my own little world out there.
"I'm not going to really pay any attention to what anybody else is doing out there, I'm just going to try and do my best."
Solid as they come
Scheffler's playing partner Hadwin meanwhile was left impressed at how the world number one had remained unflustered during a round that threatened to unravel after the triple-bogey.
"He's as solid as they come," Hadwin said. "He's the No. 1 player in the world for a reason, and he's far and above the No. 1 player in the world, I believe, especially after watching today.
"I don't expect him to lose this golf tournament - so one of us is going to have to make a run tomorrow."
Hadwin cautioned though that Scheffler's pursuers would need to be cautious.
"It's hard to be too aggressive around this place. You do that and you start chasing birdies and you'll shoot 80 before you even know it."