After parring the 18th hole, Koepka walked off the green like a man leaving the grocery store with supplies for a barbecue. Though his face did not show it, he was excited, really.
“Did you see that fist pump on 18?” Koepka said.
With his laid-back demeanor and long-hitting dexterity, Koepka has much in common with last year’s champion, Dustin Johnson, who missed the cut at Erin Hills. They are good friends, and on Saturday night Johnson phoned Koepka, who at the time sat one stroke off Brian Harman’s 54-hole lead. Their conversation was lengthy, for them: nearly two minutes, by Koepka’s estimation. Johnson reminded him to stay patient and not to get ahead of himself.
Until this past week, patience had done little to guide Koepka, who has been in a hurry since he turned pro in 2012 after a solid college career at Florida State. He eschewed the beaten path to the PGA Tour — through the Web.com circuit — to play in Europe, where he thought he could improve his game, and his world ranking, more quickly.
He joined the European Tour in 2013 and won the Turkish Airlines Open a year later. He got his first PGA Tour title at the 2015 Phoenix Open.
In an interview with Golf Digest in 2015, Koepka said that in his mind, he saw himself as part of an exclusive group with Spieth, McIlroy and Jason Day, who had just won the P.G.A. Championship three months shy of his 28th birthday. “Even though I’m not in it — nowhere near it,” he said.
Going into this tournament, he had over $10 million in PGA Tour earnings but felt an emptiness that only trophies could fill.
“I just felt like I should be winning more,” Koepka said. “I don’t know why — I just couldn’t stand the fact that I had only won once.”
The reason was no mystery to Koepka’s caddie, Ricky Elliott. “With all his peers winning that are younger than him, 27’s not old, but he thinks he should be winning every week,” he said.
The leaderboard at Erin Hills heading into the final round was an advertisement for the depth in men’s golf. The top 16 players at the beginning of play on Sunday ran the gamut from the 21-year-old Si Woo Kim to the 40-year-old Charley Hoffman. They spanned the globe from the United States to South Korea. And their résumés ranged from that of Brian Harman, who had missed the cut in five of his previous seven majors, to that of Rickie Fowler, who recorded top-five finishes in all four majors in 2014.
And none of those top 16 had won a major.
The course, too, was gracing the big stage for the first time. Erin Hills, situated 35 miles northwest of Milwaukee and carved out of rolling pastureland, was a first-time U.S. Open site. On Sunday, after three days of benign playing conditions, the wind kicked up and turned the nearly 8,000-yard layout into a bucking mule.
Jordan Spieth, the 2015 Open champion, was in the fifth of the 34 twosomes to tee off, and he tamed a course that was buffeted by 30-mile-per-hour winds with a three-under 69, his best round of the week by two strokes, and finished at one over.
The winds died down as the afternoon wore on, and Hideki Matsuyama, bidding to become the first Japanese winner of a men’s major, took full advantage. He posted the day’s low round of 66 to give the seven twosomes that started after him a target to beat: 12 under.
After a third-round 63, Justin Thomas was tied with Koepka, and facing the unenviable task of trying to follow one great round with another. At the 1980 United States Open, Jack Nicklaus and Tom Weiskopf both opened with 63s. In the second round, Nicklaus carded a 71, Weiskopf a 75.
Thomas, 24 and already a three-time tour winner this season, could not avoid a similar letdown. He closed with a 75 to finish tied for ninth at eight under with Trey Mullinax (68) and Brandt Snedeker (71).
Like Thomas, Fowler, Matsuyama and almost every other tour player in his 20s, Koepka was drawn to golf by the magnet that was Tiger Woods.
“It was pretty cool to watch Tiger win; I’m not going to lie,” Koepka said. He added, “That’s kind of why I’m playing.”
Wisconsin’s native son, Steve Stricker, who closed with a 69 to finish five under, planned to return to the course after signing his scorecard. As the American captain of this year’s Presidents Cup team, Stricker, 50, had a vested interest in how Koepka, Harman, Fowler — and even Matsuyama, a lock for the International squad — finished.
Stricker had already seen enough this past week to feel good about where the game is headed. “These guys just take on everything with no fear,” he said. He added: “They play very aggressively. And it’s fun to watch.”
Because of an editing error, an earlier version of this article misstated Rickie Fowler’s final score. He was 10-under, not nine-under. An earlier version of this article also described incorrectly the number of players to have shot rounds of 63 at the United States Open before Justin Thomas. Four golfers, not two, had shot a 63, including three before the final round. The article also misspelled the given name of Brooks Koepka’s caddie. He is Ricky Elliott, not Rickie.