Florida native Koepka becomes the seventh consecutive first-time major victor, a run started by Jason Day at the 2015 US PGA Championship.
Koepka, 27, grabbed control with three straight birdies on the back nine at Erin Hills.
Harman might be the surprise leader after three rounds at the U.S. Open, but there was nothing ordinary about his game.
Harman, bidding to become the first left-hander to win a U.S. Open, is a victor on the PGA Tour this year while Thomas is the world number 13, a three-time victor this season and a member of the exclusive "59" club after breaking 60 at the Sony Open this year. It's the first time that has happened since 1998-2000.
Thomas poured in the eagle to become the 29th player with a 63 in a major championship.
Koepka was also tied for fourth in the US Open in 2014 - albeit 10 shots behind runaway victor Martin Kaymer - and shot 71 at Erin Hills in the 2011 US Amateur, although he failed to reach the matchplay stages.
Brooks Koepka is in position to win his first major title.
Harman closed with two birdies and three tough pars for a 5-under 67 that gave him a one-shot lead at 12-under 204.
Matsuyama's 66 was the best score on a windy final day, one better than Koepka.
Hideki Matsuyama is making one last push at the U.S. Open. Only six players had ever reached double digits under par in the previous 116 times at the U.S. Open. The 27-year-old has always been considered one of the game's most promising young players.
Not to be overlooked was Si Woo Kim, who captured The Players Championship last month.
Justin Thomas shoots 63, trails Brian Harman by 1 at US Open
The low scoring suggested the 11-year-old course was a cream puff, hardly the USGA's idea of the ultimate test in golf. Thomas has a 59 to his name in 2017 - at January's Sony Open - and two of his four PGA Tour wins have come this year.
Cameron Champ was the lowest amateur heading into the final round, but he finished with a 4-over 76 to drop back to even par for the tournament. If Brian Harman can hold onto his one shot lead on Sunday, his personal coffers will swell by $2.2 million.
Rickie Fowler was two behind Harman on 10 under after a four-under-par 68 which kept him firmly in contention.
CINKING IN: Stewart Cink had a bad start to the third round of his 20th U.S. Open. Champ is 3 over in the final round with two holes to play.
Scheffler plays for the University of Texas, and Champ plays for Texas A&M.
And the prime beneficiary was Thomas, who catapulted up the leaderboard with his record-breaking nine-under-par 63.
Fleetwood began the day in a tie for second and made an encouraging start with a birdie from eight feet on the second.
It was at the U.S. Open three years ago when Koepka tied for fourth that helped earn a PGA Tour card, and he powered his way from obscurity to his first PGA Tour victory in Phoenix, his first Ryder Cup team last fall and now a major championship.
"Tomorrow will be fun and special, just going around here and being a part of this first U.S. Open here in Wisconsin", Stricker said.
Koepka birdied his first two holes to get to 13 under.
They fearlessly attacked the pins and nobody was more ruthless than Thomas, who ripped apart the links-style layout carding nine birdies and two bogeys before capping his record-smashing effort by coolly rolling in an eight-foot putt for eagle at the par-five 18th.