Thomas poured that in to become the 29th player with a 63 in a major championship.
Thomas' historic round included nine birdies, including three straight to finish the front nine.
Li turned professional at age 16 and won the Volvo China Open last year on the European Tour, securing a two-year membership and qualifying for the Rio Olympics.
McIlroy, playing for the first time in a month to rest a nagging rib injury, finally got it going when it was too late.
Brooks Koepka is closing in on the U.S. Open title.
The 28-year-old from Murrieta, California, carded seven birdies to lead by one stroke at the end of the first round. Not enough experience in major championships. "This went totally against the tradition of the U.S. Open".
Koepka made three birdies over his last seven holes for a 68.
Scottie Scheffler is the low amateur for this year's U.S. Open. But a trip into the fescue grass after a wayward tee shot cost the Australian a double-bogey and he ended tied-17 at four-under par, probably out of the hunt with a round to play.
Fowler was among those who wouldn't mind seeing the conditions toughen up for the final 18 holes. And if you'd think the 30-year-old Savannah native might be intimidated by the big stage on Sunday afternoon, consider: Harman's already beaten Rickie Fowler head-to-head once. He is at 11 under, two shots ahead of Charley Hoffman and Tommy Fleetwood.
The race for low amateur at the U.S. Open is down to Cameron Champ's last two holes. He played on two Walker Cup teams.
Scheffler plays for the University of Texas, and Champ plays for Texas A&M.
Thomas became the fifth player to shoot 63 in the U.S. Open, and the first with a score of 9 under. Another dropped shot at 15 left him five off the pace.
It was a much different scene than Saturday, when Thomas matched a major record with a 63. Harman missed the cut in his previous two U.S. Opens.
But the third-round leader at the U.S. Open? Not only that, he gave Erin Hills a piece of his mind, basically stating that the course is a reason why Thomas' score wasn't as significant.
Positioned 299 yards from the pin on the par-5 18th, and needing to hole out the shot to make the weekend, he lashed at a 3-wood that hit about pin high, then rolled off the back of the green.
"It's been an off-week for me with the putting", said the former world number one.
While stronger winds are expected on Sunday, Thomas - yet to finish in the top 10 of a major - said the soft greens during the third round helped. And then he made birdie on the next hole.
Harman might be the surprise leader after three rounds at the U.S. Open, but there was nothing ordinary about his game.
Jordan Spieth has finished his U.S. Open on a high note.
He also said Erin Hills "isn't exactly Oakmont". Brian Harman doesn't have a chance, they'll say.
And yet, Thomas won't even walk to the first tee box Sunday with the lead. "My grandmother had lived in the same area - she lived in Delafield, Wisconsin, which is just south of the area where Erin Hills is".