“I hit it about as hard as I could,” Koepka said of the massive three-wood shot that carried more than 300 yards to set up his eagle.
Australian Adam Scott, another late charger, was a stroke back of the leaders after a 64, with world number one Dustin Johnson (67) and Bryson DeChambeau (66) tied for fourth at eight-under 134.
Woods, two weeks after being runnerup to Koepka at the PGA Championship, stayed alive in the FedEXCup playoffs with a repeat 71 that left him right on the projected cut at even par and 10 strokes back.
A three-putt bogey at the last had him sweating as to whether his tournament was over.
"Golf’s one of those things where you just have to make putts. I mean, no matter how good. You hit your golf ball tee-to-green, still got to hole it," Woods told Golf Channel after needing 35 putts.
"Today was one of those days when I didn’t make anything."
Phil Mickelson, who will go head-to-head with Woods in November for a $9 million winner-take-all event, putted much better than Woods, making six birdies in a round of 68 to land four strokes off the lead at 136.
First round co-leader Lovemark enjoyed a four-shot lead at one point before former champion Scott and then Koepka charged home.
Scott, playing ahead of Koepka and with four birdies on the front nine, bounced back from a bogey at the 10th to deliver four more birdies, three in a row from the 12th, to pull within one of Lovemark.
"I felt like I had everything under control today," said Scott. "Really important stretch around the turn for me. I bogeyed 10, then made a really good par save on 11 and got back on the horse where I wanted to be."
Then along came U.S. Open and PGA champion Koepka.
A mixture of two birdies and two bogeys had left him at even par for the day through 11 holes.
But the three-times majors winner found another birdie at 12, then sank a 22-foot putt for the eagle before closing the round with three consecutive birdies.
“If I’ve got the feeling," Koepka said. "I’ve simplified the game so much. There’s no swing thought. There’s no anything. I’m not trying to work on anything while I’m out there. I’m just trying to hit the correct shot."
(Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Ian Ransom)
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