Then on the uphill par-3 11, he flew his tee shot over the green, chipped out of deep rough and watched his ball roll into a bunker, blasted out and sank a 15-foot putt for bogey.
A year after he marched to victory with a 16-under total at Erin Hills, Koepka kept his nerve on the back nine to emerge with a one-over-par total of 281.
Fleetwood must console himself with a cheque for $1.2m and a share of history. But after almost equalling the best ever round in a major of 62 he was pleased with his day's work. He returned to practice, found his form relatively quickly, and set out to win again, maybe even a second straight U.S. Open.
"I had chances the last few holes to shoot 61 or 62", he admitted, knowing the record in a major is Branden Grace's 62 at last year's British Open. Little did he know it was also ultimately be for a spot in a playoff.
"We said last night 'shoot the greatest score in the US Open and you'll have a chance, '" said Fleetwood, 45 years to the day after Johnny Miller posted the first and only other 63 in the final round of a US Open.
"This is incredible. I don't think I could have dreamed of this, going back-to-back".
Tony Finau, who played alongside Daniel Berger in the final pairing of the day, finished fifth after making a sloppy double-bogey on 18.
Fleetwood, playing more than two hours ahead of the overnight leaders and starting the day six shots off the pace, had threatened to steal a stunning victory after reeling off four consecutive birdies from the 12th hole.
Even after the USGA Chief Executive Mike Davis came on the air late in the afternoon to admit the association made a few mistakes and allowed good shots to be penalized, it isn't clear that they really know where the line between hard and unfair really lies. It's amusing though, when you finish, you always feel like you're going to be just short [of winning].
Yes, it drove him insane not to play, especially not being able to compete.
The uncomplicated Koepka, playing the final round with his close friend Dustin Johnson, never looked fussed or bothered, which is his way.
"I always feel like I'm overlooked".
U.S. Open just takes so much discipline, he said. "I feel like it was on the line, and I think some of the pin placements were over the line".
USGA CEO Mike Davis asked for a "mulligan" after Saturday's round, which didn't appease at least one golfer.
There have been exceptional golfers who have spent their lives unsuccessfully chasing big titles, however Koepka seems to have a gift for these big moments, often walking away with success. Henrik Stenson (74) made the turn at 1 under and shot 40 on the back nine. I miss competing. I've got to be competing at something.
Finau, a victor at the 2016 Puerto Rico Open, said he wouldn't be trying to change his aggressive style despite some costly errors. Fowler was 19 shots better than his 84 in the third round, the highest score in his U.S. Open career.
"I've got nothing but respect for how well Brooks did, just to hole the putts at the right time".