Despite posting that record-low number, Thomas still has work to do. Then there will be a playoff round on Monday.
Don't try this at home.
Elsewhere, Masters champion Sergio Garcia finished with a 71 to stay on six under, six behind Harman. It dropped him two shots off the lead and, to add insult to injury, it will still count as a three-putt.
Fleetwood was alongside Reed after a birdie on the first but Casey tumbled down the leaderboard after following an opening birdie of his own with a triple-bogey on the third. "You've seen 5, 6, 7, 9-under out there".
Around 70 minutes earlier, compatriot Patrick Reed had faced a similar length putt to Thomas on the 18th to shoot eight under but missed his birdie attempt and had to settle for a 65.
If you'd thought you could spend a politics-free afternoon by attending the U.S. Open in Middle Of Nowhere, Wisconsin, well, that's wishful thinking anymore. Rickie Fowler accomplished the feat in the first round, and Hideki Matsuyama and Chez Reavie hit the number Thursday. "But I'm looking forward to getting the job done". He two-putted for birdie, and he rolled in a 25-foot birdie putt on the 17th.
No matter which direction or how hard the wind blows, you can probably expect a finish unlike most U.S. Opens.More news: Portugal forest fire victims die in their cars as flames engulf road
Koepka tied for 13th in last year's Open at Oakmont. His best finish was a tie for 37th previous year at Oakmont.
Jordan Spieth's first attempt to get out of the bunker on the 18th hole Saturday ended badly. But he saved his best for the final four holes.
Stricker shot a 69 to move to 2 under going into the final round.
Not at Erin Hills, which has been left defenseless this week by soft winds and even softer conditions. He just has to listen to the crowd.
"For one, the greatness of my round is the 63 in the last round of the U.S. Open to win by one", said Miller, now an analyst for the American TV network NBC. He's one shot back of the lead shared by four golfers who tee off later Saturday.
"It's been an off-putting week for me", Spieth said. The ball slid back down the sandy slope until it came to a rest near his footprints.
CINKING IN: Stewart Cink had a bad start to the third round of his 20th U.S. Open. Harman had back-to-back birdies on 14 and 15 before closing out with three straight pars to take over the lead. Champ tees off later Saturday.More news: Worth the Upgrade: The new iPad Pro
Thomas had 300 yards to the hole for his second shot at the 18th.
Low scores were available. Will Erin Hills continue to cough up birdies in abundance, or will it finally toughen up? Not everyone can take advantage.
The lead, however, belonged to Brian Harman.
Zach Johnson holed an 8-foot putt on the par-3 ninth for his third birdie of the front nine.
The flag commemorates the late Arnold Palmer's win at the 1960 U.S. Open at Cherry Hills.
The U.S. Open is wide open going into the weekend.More news: GOP Lawmaker Scalise Still Critical Though Doctors `Encouraged'
- Paksitan vs India, ICC Champions Trophy final
- United Kingdom police warn use of fake explosive belts is 'new tactic'
- Tapwrit Outlasts Irish War Cry in Belmont
- Sadiq Khan: Grenfell fire shows 'gaping hole' in government response
- Kohli turns off social media ahead of Pakistan clash
- Why Trump can not fire Federal Bureau of Investigation special counsel Robert Mueller
- Putin, Saudi King Discuss Qatar Diplomatic Crisis
- Deputy AG: 'Americans should be skeptical about anonymous allegations'
- A glance at the Senate's Iran, Russia sanctions legislation
- Morata tells Bale to join him at United