The two-time US Open champion followed his record-equalling second-round 63 with a four-under 66 on Saturday, lifting the American to 12 under and two strokes clear of nearest challenger Adam Scott.
He did just that over the first nine holes, making five birdies on the front nine on the way to a 31 that drew him within two of the lead.
Well, it depends on how you look at it. It would be the first time Woods would have won a major without a lead or co-lead going into the final round.
"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".
Woods failed to convert on both, despite having given himself excellent chances.
At the 17th, after ramming his eagle putt through the break, he missed the 4-footer coming back. It was a massively squandered opportunity, one that could easily have seen him grouped with Koepka in the final pairing.
The ball sailed right into the trees and hit a cart path, cannoning deep into the woods.
Gary Woodland almost buried his PGA Championship hopes in sand with a triple bogey horror show in the bunkers on Saturday but dug himself out of trouble to remain in contention for a first major title. It has happened in some form at all of those tournaments, and it happened again on Saturday at Bellerive.
"It was meant to be that I was the first Aussie to win the Masters and it is hard to get my head around that when I think of everything that went before me". While Woods was unable to close out a win at The Open last month, he did lead on Sunday entering the back nine. It is a trend he has yet to buck.
It left a sense of anti-climax, but Woods is still within reach of his 15th major, a situation few would have predicted at the start of a year which has seen the 42-year-old resurrect his career after debilitating injuries. Koepka appears fearless with the driver. Glenwild Golf Club's Craig Hocknull shot 72-73 and Davis Park Golf Course's Zach Johnson posted 76-69. Tiger's driver still remains a liability.
Woods didn't discount the fact that the long day might have had an impact. A lot needs to go right.
Finau completed his adventurous second round Saturday morning, finishing with 10 birdies in a 4-under-par 66 that was good enough to make the cut.
Only a three-putt bogey at the fifth hole halted his progress, though he put the setback quickly behind him to birdie the next three holes.
He never imagined what it would take for him just to get to the weekend. However, the Jayhawks won four of their last six games played in Columbia.