McIlroy is now eight shots adrift of Japan's world number 10.
Saturday is known as "moving day" in golf parlance but in the case of McIlroy, who started the day six behind the Japanese world number 10, it was in the wrong direction.
The world number three got to the turn at three-under for the round, including an astonishing birdie at the long eighth hole.
But the FedEx Cup champion saw the course claw all his gains back before birdies at 16 and 18 gave him some consolation.
McIlroy finished at nine under in a tie for eighth place after a 70, but is now eight shots adrift of Japan's world number 10.
Matsuyama sprayed 19 birdies and six bogeys all over the course with memorable attacking golf during his first 36 holes, but he reined in his aggressive instincts Saturday to card a bogey-free four-under 68 and move to 17-under par.
"The first two days, making lots of birdies was a lot of fun," the quietly spoken 24-year-old told reporters through an interpreter.
"But today, when you're in a position to win, playing smart and making no bogeys was very satisfying."
Matsuyama started the day three shots clear of Russell Knox and maintained the margin courtesy of a crucial birdie at the final hole.
"It was a big, big birdie to take the lead from two strokes to three," said Matsuyama. "I had 248 yards to the pin. Faded a three-wood in there."
The first Japanese player to make the world's top 10 since Jumbo Ozaki in 1998 is bidding to become the first Asian to win a World Golf Championships event.
But he will face a fierce battle from defending champion Knox, who will make his own piece of history if he can be the first player to retain the Old Tom Morris Cup on Sunday.
"I'm not going to give up my title without a big fight tomorrow. I look forward to every minute and see what happens," said Knox.
McIlroy had seemed ready for a charge when he got off to a fast start with birdies at the second and sixth holes.
His third birdie, at the par-five eighth, came under the most remarkable of circumstances. At that point it seemed as if it would be the Northern Irishman's day.
Going for the green in two, McIlroy slashed the ball so far right that it cannoned into trees and across a cart path.
Faced with a tiny gap in thicket and no green to work with, McIlroy somehow fizzed a low wedge through the branches hard into the bank of a stream guarding the green and watched it hop up obligingly onto the putting surface.
He calmly rolled in the 15-footer for birdie and allowed himself to laugh, knowing he had dodged a bullet.
But the course bit back after the turn as bogeys at 11 and 12 were followed by another at 15 before his finishing flourish left him in a six-way tie for eighth place.