A chaotic afternoon at Augusta National saw both men plunk key shots into water on the back nine but finish level atop the leaderboard on 11-under 205 through 54 holes, one stroke ahead of American Sam Burns.
McIlroy, who started the day with a record six-shot lead, carded a one-over-par 73 while Young roared into contention with a scintillating seven-under-par 65.
"I didn't have it today," McIlroy admitted. "I scrambled a lot on the front nine."
Second-ranked McIlroy birdied the 14th and 15th holes to regain the lead but found the trees off the 17th tee on the way to a bogey and his one-over round.
"This golf course has a way of, when you're not quite feeling it, you struggle," McIlroy said. "You have to dig deep.
"I still have a great chance," McIlroy added. "I'm in the final group. That's where I want to be.
"I need to be better tomorrow. If I'm going to win tomorrow, I have to be better than I was today."
McIlroy, a five-time major winner, hopes to match Tiger Woods, Jack Nicklaus and Nick Faldo as the only back-to-back winners of the green jacket.
Third-ranked Young, last month's Players Championship winner, got off to a scorching start with birdies on five of the first 10 holes.
He birdied 13 and 14, his drive at the 13th hitting a tree and landing fortuitously in the fairway, then overcame a watery bogey at 15 by curling in a 27-foot birdie putt at the par-three 16th.
As a result, the 28-year-old American has a prime chance for his first major title.
"There certainly is no lead that's safe out here, but Rory loves it here, and no one would be surprised if he had shot 65," Young said.
"It's just one of those times that if he doesn't, we have to take advantage, and I got myself here today."
Burns carded a 68 and was one stroke in front of Ireland's Shane Lowry.
Lowry makes hole-in-one, Scheffler 'in position'
Lowry aced the 190-yard par-three sixth hole on his way to a 68 that left him in fourth on 207, one stroke ahead of Australian Jason Day and England's Justin Rose.
Lowry, the 2019 British Open winner, became the first Masters player with multiple holes-in-one, having aced the 16th in the final round in 2016.
"That's wild," Lowry said. "You don't ever expect to make a hole-in-one. I just couldn't believe it. You're out there, and you're in the hunt at the Masters, and you're making a hole-in-one. It's pretty cool. It was obviously amazing."
World number one Scottie Scheffler fired a bogey-free 65 - his lowest career Masters round - to stand four off the lead on 209 alongside China's Li Haotong, who also found water on his way to shooting 69.
"I put myself in position," Scheffler said. "I just need to get the job done."
McIlroy made double bogey at the 11th when his approach sailed left into a pond, and after a bogey at the par-three 12th, his lead had vanished in Amen Corner.
McIlroy responded with a 19-foot birdie putt at the 14th and drove the green in two at the par-five 15th to set up a tap-in birdie, only for a bogey at 17 to drop him back.
"I knew today wasn't going to be easy," McIlroy said. "The quality of the chasing pack was very good, and a lot of guys played their best golf."
Rose, a three-time Masters runner-up hoping for a green jacket at age 45, went from seven adrift to three back and hopes for a final round like last year when he made 10 birdies.
"It's going to take a special round tomorrow, so there's a chance, which is great," Rose said.
"I'm going to try to channel a bit of last year and see what happens."