His six-under 64 on Sunday was his best single-round score of the tournament.
Woods' title hopes largely ended on the 17th tee. He recovered after a disastrous drive well right of the fairway to salvage a par. But that offered little respite after Koepka birdied Nos. 15 and 16 to move to 16 under.
Woods birdied No. 15 after his approach left him within a few feet of the cup to leave him with a tap-in for 13 under. The ball almost came to a complete stop as it landed on the green:
Good luck is almost always required for a golfer to win a major tournament. CBSSports.com's Kyle Boone wondered whether it simply wasn't Woods' day after his par putt on No. 14 lipped out:
The bogey on No. 14 dampened some of the excitement for fans who have been following Woods' every move, which was why getting that shot back one hole later was big for the 42-year-old. His inability to make up any ground on Koepka on the 16th and 17th holes, however, stung almost as much as the bogey on the 14.
Barring a historic collapse by Koepka over his final two holes, Woods' late surge will come up short.