Overnight leader Fitzpatrick bounced back from a shaky start, holing out from off the greens on 14 and 15 for birdie and eagle, respectively, to finish three strokes clear on 17-under-par at Hilton Head Island in South Carolina.
Having bogeyed the first and third holes, the 2023 RBC Heritage champion clicked into gear around the turn, becoming the only player this week to drive his ball onto the ninth green, with a 338-yarder that he converted for birdie.
Fitpatrick reclaimed the solo lead with a confident 10-foot putt on the 12th.
The Englishman putted in a bobbling left-to-right effort from 26 feet off the green for another birdie on 14 - the same hole on which he had bounced off a tree on the way to an improbable birdie a day earlier.
And he then executed a perfect chip into the hole from 30 feet on 15 to open a three-shot lead.
"It's always satisfying when you can turn it around, particularly if you have not played that well," said Fitzpatrick.
Fitzpatrick is seeking his fourth PGA Tour title, adding to last month's Valspar Championship and the 2022 US Open, as well as his 2023 RBC Heritage title.
"Obviously, it would have been nicer to go out with nine birdies... and be plenty clear," he said.
"But to be in the position I am tonight, obviously it's something that you'd snatch your hand off for."
Scheffler - having begun Moving Day seven strokes off the lead - made five birdies in his first six holes to soar into contention.
"You can't ask for much of a better start than that. Came out, nice birdie on the first, good birdie on the second. Kind of stole one on four, and two good birdies there on five and six," he said after.
From a stunning front-nine 31 that shot Scheffler briefly up to tied-first, the four-time major winner's momentum slowed slightly with a string of frustrating pars.
But he birdied the 16th and final holes for a seven-under round of 64, to finish 14-under-par for the tournament with one day to play.
"As you start kind of getting back into contention, I think that's always fun. It's never as fun being on the outside looking in," said Scheffler.
Meanwhile, fellow American Brian Harman hit the day's best round with a career-low 63 at windy Harbour Town Golf Links, featuring nine birdies.
The Savannah-born golfer thrived in familiar local conditions, finishing with three straight birdies after holing a bunker chip from 30 feet on 17.
"Just tried to keep the pedal down. It's going to take a low number to win," said Harman.
Norway's Victor Hovland, who had started the day one stroke off the lead, had a disastrous start, including a bogey on the first and a double bogey on 3.
He finished a disappointing day six strokes back with a round of 73.