"At the beginning of the year", he said, "if you would say I would have a legit chance to win the last two major championships, I-with what swing?"
The 14-times major victor, who had whipped the massive gallery into a frenzy on the front nine, sent them into absolute hysteria with two more birdies at 12 and 13 that again vaulted him within one of the lead.
"And I was playing with Scotty, so I knew what I was up against". But he recovered with birdies on three of the next four to finish with a 1-under 69 on Sunday and 10-under 270 overall.
Yet there he was on Sunday of a major championship, right in the hunt - with Woods, no less.
But Scott missed a crucial birdie putt at the par-5 17th, which would have cut Koepka's lead to one, before a sloppy bogey at the 18th. He made up for it with laser-like iron shots like the one he hit to kick-in distance at the par-4 15th, and a tidy 23 putts. The uphill effort looked good the whole way before stopping on the edge of the hole, unwilling to fall in despite heartfelt pleas from the player himself and the raucous St. Louis crowds.
"Looking back, I don't think it was so much the game - it was just energy-wise I was really struggling this week", he said. The round, equaling his lowest of this comeback season, will likely not be good enough to win major number 15, but he had a legitimate chance to win for the second consecutive major after tying for 6th at last month's British Open.
Woods huffed and puffed with everything he could muster but in the end could not quite blow down the Brooks Koepka house at Bellerive, coming up two shots short.
Koepka's lapse also brought many more players into the frame, with halfway leader Gary Woodland, Spain's Jon Rahm and Rickie Fowler on nine under and Woods four off the pace alongside defending champion Justin Thomas, Ireland's Shane Lowry, Jason Day, Stewart Cink and Charl Schwartzel.
"I'm just pleased with what I've done so far, and now to be part of the Ryder Cup conversation, from where I've come to now, it's been pretty cool", said 14-time major champion Woods.
"I was feeling really good out there, especially as he back nine got going", Scott said.
It is the Koepka's third major title in 14 months and second this year, having successfully defended his breakthrough 2017 US Open victory at Shinnecock Hills in June. I had a flawless number and I have been hitting my three wood unbelievably well all week and I just hit a bad shot. He joined Woods, Jack Nicklaus, Ben Hogan and Gene Sarazen as the only players to win the two US majors that rotate to different courses in the same year. I warmed up hitting it left, I was hitting it right. He parred No. 16, couldn't birdie the par-5 17th because of a wayward tee shot and rolled in a 19-footer for birdie on No. 18 to put some pressure on Koepka. "I played 29 holes in the heat".