The nearest challengers to Harman include a man who made history on Saturday with the lowest score to par in U.S. Open history.
Justin Thomas, coming off a 9-under 63 that matched the major championship scoring record and was the first 9-under round at a U.S. Open, went out in 39 and closed with a 75 to tie for ninth.
The world No.13 will hope to follow up Saturday's record-breaking round by capturing the first major title of his career and he is confident of landing the top prize, revealing he is enjoying the set-up at Erin Hills. "It's all pretty self-explanatory in terms of what it means". But there's a couple today where I kind of puffed them out there and I'm back there a couple extra clubs.
Brian Harman leads at 12 under.
The par-four third hole proved the toughest on day three, with a tricky pin position at the back of the green contributing to 20 bogeys, two double bogeys and just two birdies for a scoring average of 4.368. He capped his round with a brilliant 3-wood from 310 yards and made an 8-foot eagle putt.
"I have a lot of hard times in a major". I want a U.S. Open where some poor person in the production truck is forced to hover his finger over the mute button all day, because players can't stop cussing about their misfortunes.
The challenge today for the leaders will be dealing with the enormity of winning the US Open.
Kaymer got the good end of the draw when rain arrived at Pinehurst No. 2, and he opened with rounds of 65-65 to reach 10-under 130 and build a six-shot lead going into the weekend.
Koepka is trying for his first major championship.
Thomas, who had six birdies on his outward nine on way to nine-under 63 on Saturday, found plenty of trouble on Sunday going three-over through the first nine to drop six off the lead.More news: Republican baseball practice gunman 'had list of names'
Florida native Koepka becomes the seventh consecutive first-time major victor, a run started by Jason Day at the 2015 US PGA Championship.
Thomas was already on course for a share of the lead as he stepped up to the 18th having carded nine birdies against two bogeys in a spectacular round.
"I've been there a handful of times and had some good finishes but I'm looking forward to getting the job done".
He rolled in an 18-foot birdie putt on No. 5 from the edge of the green that broke so severely that he stood with his toes facing the hole and rapped the ball toward his left foot.
"It doesn't matter how long, how whatever the course is", Thomas said about the longest course in major championship history.
Gusts are forecast to pick up on Sunday, when a new major victor appears all but certain to be crowned with none of the top 16 on the leaderboard having previously taken out one of golf's premier strokeplay events.
"I'm looking forward to hearing about that when I get back to the house since J.T. and I are staying together", said Fowler.
Of the five other players who shot a 63 in the third round at a major, none went on to win.
It was all part of a dizzying day at the U.S. Open where at times the leaderboard resembled a game of musical chairs with names moving up and down.