Brooks Koepka watches his shot from the ninth tee at Shinnecock Hills Golf Club during the final round of the U.S. Open on Sunday in Southampton, N.Y. Koepka closed with a 2-under-par 68 to finish at 1-over 281 and win by a stroke over Tommy Fleetwood.

SOUTHAMPTON, N.Y. — One was about power. The other was about patience.

Brooks Koepka has a game for the U.S. Open — no matter the course, no matter the test, no matter the circumstances.

The tournament's 2017 champion never lost hope when he began his bid to repeat with a 5-over-par 75 on Thursday and was 7 over midway through the second round Friday. He didn't lose his mind Saturday in the most punishing third round of a U.S. Open in nearly two decades.

And with a cool head and a hot putter, he didn't give anyone a chance down the stretch Sunday at Shinnecock Hills Golf Club.

Koepka pulled away from a four-way tie for the lead with three birdies in five holes, held off Tommy Fleetwood and his record-tying 63 and closed with a 2-under 68 for a one-shot victory to become the first repeat U.S. Open champion in 29 years.

"I don't want to say I didn't think I could do it," Koepka said. "But I knew that it was going to be that much more difficult. And to finally do it, it's much more gratifying the second time. I can really appreciate how hard it is to win a major."

Last year, Koepka won with birdies at spacious Erin Hills near Milwaukee. The signature moment from this U.S. Open was a trio of putts to escape trouble on the back nine — two for par, one for bogey.

"I enjoy being pushed to the limit," Koepka said. "Sometimes you feel like you are about to break mentally, but that's what I enjoy. I enjoy hard golf courses. I enjoy playing about the toughest in golf you are ever going to play."

Shinnecock Hills was every bit of that, particularly on Saturday, when conditions were so severe the last 45 players to tee off shot over par. The United States Golf Association conceded the course was over the top and pledged to add water to slow it down. Fleetwood raced into U.S. Open history with a 63, despite not making birdie on the two par 5s and missing an eight-foot birdie putt on the final hole.

That cost him more than sole possession of the record. It cost him a chance at a playoff.

Koepka took a two-shot lead with a wedge shot that landed 3 1/2 feet from the hole and set up a birdie putt on the par-5 16th, allowing him a safe bogey on the final hole to finish at 1-over 281. It was the first time since the 2013 U.S. Open at Merion Golf Club that no one broke par for the tournament, and it was 13 shots more than his winning score at Erin Hills.

Curtis Strange, the last player to go back-to-back in this major in 1989, watched the entire final round as the Fox Sports reporter on the ground, and he and Koepka shared a brief hug off the 18th green.

"Hell of a job," Strange said to him.

Fleetwood was one shot behind when he finished, and Koepka still had 11 holes to play as Shinnecock Hills began to get crisp under another sunny sky. With a putting performance and calm demeanor reminiscent of Retief Goosen when he won the previous U.S. Open at Shinnecock Hills, in 2004, the 28-year-old Koepka began the back nine with three pivotal putts — one for birdie, one for bogey, one for par.

The biggest might have been his bogey on the nasty little par-3 11th. Koepka pulled a pitching wedge to the left, down the slope and into thick grass. He chopped the ball up the slope with so much speed that it raced across the green and into the bunker. He then blasted out to eight feet from the hole and made the putt to keep his lead at one shot.

"I think that was like making a birdie, maybe even making an eagle," he said. "Because it could have been a big momentum shift there, and we could have been playing tennis, just going back and forth. To make bogey there was pretty incredible, and I think kind of the reason why we won."

He wasn't through. He hacked out of the hay over the green at No. 12, pitched beautifully to seven feet from the cup and made the par. Two holes later, after another drive into grass so thick he wasn't sure he could get it out, Koepka rolled in an eight-footer for another par save.

Dustin Johnson, part of the four-way tie for the lead to start the final round, was one shot behind at the turn until a trio of three-putt bogeys on the back nine. A birdie on the final hole gave him a 70 to finish alone in third.

Masters champion Patrick Reed flirted with the second leg of the Grand Slam. He was tied for the lead when he ran off five birdies in his opening seven holes. Reed spent too much time in the high grass on the back nine, though, and closed with a 68 to finish fourth.

Fleetwood played with Koepka in the final group last year at Erin Hills. He finished his round as Koepka was wrapping up on the par-3 seventh.

"The best players in the world are up there trying to win a U.S. Open, and watching them down the stretch, you've got nothing but respect for how well Brooks did, just to hole the putts at the right time," Fleetwood said. "He kept it together, and he's a world player. He's one of the best players in the world.

"It wasn't great for me, but it was great as a golfer to watch how he did it."