They led by one stroke from American Xander Schauffele in the third of four playoff events on tour. Compatriot Bryson DeChambeau, a winner in the past two weeks, opened with a 67.
The key to Woods' score was assured putting with the old Scotty Cameron putter he brought out of mothballs after wielding it in 13 of his 14 major victories more than a decade ago.
"I’ve been monkeying around with it at home in the backyard through the summer. It just never felt right, but it feels good (now)," the American told reporters as a river of sweat poured down his flushed face.
"I know the release point and I know how it swings and my body morphs into a position where it understands where it needs to be to release the putter, because I’ve hit hundreds of millions of putts with that thing."
Woods has shot 61 four times on the PGA Tour, most recently at the 2013 Bridgestone Invitational which he won for his 79th career victory on tour, but he is still stuck on that mark.
McIlroy threatened to steal the headlines from Woods. Playing the back nine first, the Northern Irishman made six straight birdies from his ninth hole, the 18th, to go nine under and raise the possibility of shooting 59.
But consecutive bogeys at his 16th and 17th holes put paid to that notion, before he birdied the par-five ninth after hoisting a five-wood second shot to the heart of the green.
WEDGE PLAY
McIlroy credited his score to improved wedge play.
"It’s been something I’ve been struggling with all year and it’s been much better the last couple of weeks," he said.
"I saw some really good signs last week in Boston and I’m continuing to see good signs this week.
"Everything was firing today. Eight-under-par was good. Probably should have been a bit better. It's still a great round."
Earlier, Woods rushed to the turn in 29 strokes, including a five-foot eagle at the par-five 16th.
"This was the shot of the entire day, a three-iron from 230 (yards) and I just laced it up in the air," the 42-year-old said. "Boy, shooting 29 on the front nine helps."
Another birdie at the first hole, his 10th, took Woods to seven under.
His only bogey came at the par-three eighth, where he misjudged his tee shot and sent an eight-iron over the back into punishing rough.
But Woods made amends with a closing birdie at the par-five ninth, where he sank a seven-foot putt.
Though he has not won since 2013, Woods missed most of four seasons with a chronic back injury before surgery last year alleviated the problem.
(Reporting by Andrew Both in Cary, North Carolina, editing by Ed Osmond and Ken Ferris)
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