The 26-year-old from Florida shot a brilliant eight-under-par 64 to reach 13-under for the tournament despite closing with a bogey on the ninth hole.
What looked like a perfect second shot landed on the green of the toughest hole on the golf course, but rolled back in the water.
Poland's Adrian Meronk, winner of three titles last season, shot a bogey-free six-under 66 to join England's Andy Sullivan (67) in joint second at 10-under par.
World number two McIlroy, a three-time winner of the tournament, is 10 shots behind Young.
The Northern Irishman hit a round of 70 including five birdies but dropped shots with three bogeys on the eighth, ninth and 11th holes to sit on three-under par.
Despite numerous close calls with a second place at the British Open in St Andrews in 2022, and tied third in the PGA Championship that year, Young has yet to break through on the highest level.
"That weighed on me for a while and at this point, I honestly don't care," said the world number 25.
"Well, I care, but it's not something that defines how I'm doing and how I'm playing.
"It would be great if I win. I am playing golf good enough to win a tournament and to win a major. I am sure it'll change at some point. I'm just happy for my game."
'Putted fantastic'
On Friday, he started from the 10th tee and made five birdies before the turn and added another four on the more difficult front nine.
"I putted fantastic. I made a couple of long ones yesterday and then made a few more today that had no right going in," said the American.
"One of those days where you kind of have a couple 30-footers and you look up and they are going right in the middle, which doesn't happen all that often."
Denmark's Hojgaard twins – Rasmus (70) and Nicolai (69) – were tied for fourth alongside Scotland's Richie Ramsay (68), three shots further behind at seven-under-par.
Luke Donald, Europe's Ryder Cup captain, made a hole-in-one on the par-3 fourth, hitting an eight-iron shot from 183 yards.
It was the third ace from the former world number one in competitive play, who hit a round of 71 for the second consecutive day.
Now a Dubai resident, Meronk picked up three shots on either side of the golf course and managed the tougher afternoon conditions really well.
"It was tricky out there. The course got firmer and firmer and the greens were fast. Just played really solid from tee to green and holed a lot of good putts," said world number 50 Meronk.
"The experience gives you a little more confidence that you've done it before, so you can do it again. The key is just to stick to your game plan, trust your shots, and be fully committed."
Sullivan made five birdies in his first eight holes and looked unstoppable at one stage. However, he cooled down with just one birdie and one bogey in his last 10 holes.
"I didn't think I would ever come off disappointed sitting at ten-under after two rounds, but after that start today, I made three pars on the three par-5s on the back nine," said the Englishman, who finished second here in 2016.
The halfway cut fell at even-par 144 and 74 players made it to the weekend.
