After changing his sweat-soaked shirt, Woods lost ground with a three-putt bogey on the fifth, but bounced back in style with birdies on the sixth, seventh and eighth.
When Tiger fanned his drive well right of the fairway two holes later, the groans were just a palpable.
"If you look at it, I left pretty much every single putt short on the back nine", he said.
"I feel like I played well today", said Woods, who only returned to competitive golf in November after undergoing spinal fusion surgery in April previous year. I got to give it a rap up the hill, it's steep, I know that -- there wasn't a whole lot of grass over there on the right side of the green and I thought that I should have played it faster than what I was thinking.
After atoning for his earlier misses with birdie putts from 10 feet and six feet on 15 and 16, Koepka offered a glimmer of hope to playing-partner Scott when he misread his putt for a four on the 17th, but the Australian could not take advantage as he lipped out from close range.
Woods just missed reeling off three straight birdies at the start of play.
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"And I really hit some great shots the next couple of holes, gave myself a lot of chances for birdie, and made a couple of them". He has not made a putt of longer than 17 feet over three days, and has only made five putts of more than 10 feet all week.
Throughout all of the heroics and histrionics, Koepka remained unfazed, some might even say indifferent to what on any other Sunday would have been a glorious exclamation point to a long-awaited comeback.
Woods, meanwhile, kept himself in the hunt for a first major victory in over 10 years as he turned in 32 with four birdies and one bogey, and he pulled within one of Koepka with further gains at 12 and 13 to set the pulses racing among the vast galleries following the 42-year-old. It was his 100th start on the PGA Tour, and the win his third major title. Players from all over the world said the enthusiastic crowds have been making it fun for them to play-despite the heat, storms and weather delay.
"I couldn't hear it", smiled Koepka, tongue firmly planted in cheek.
If he's being honest with himself, Tiger would have had to shoot 62 to even force overtime and even that probably wouldn't have been enough considering Koepka's mastery of a game that, however ironically, Tiger invented.
"I didn't have a swing at the time". My putting was OK. He certainly gets points for showmanship and a willingness to attract some eyeballs, but he doesn't quite get full marks for creativity; Brown said he remembered seeing another fan do something similar about a year ago, and decided this would be the ideal time to go for it. "So it's been a hell of a process for sure".
But then the golfing gods gifted this marathon Saturday out of left field and left us all with a Sunday at colorless and faceless Bellerive that could be the most memorable golf event of the year, and of many years to come.