McIlroy had been a shot clear of Woods at nine-under par after 15 holes when Woods headed for the clubhouse.
McIlroy credited his score to improved wedge play. Yet Woods has rarely been out in front.
"It was one of those days where it was out there", McIlroy said.
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.
"I saw some really good signs last week in Boston and I'm continuing to see good signs this week".
Woods managed an eagle and seven birdies and his only hiccup being a late bogey on his back nine at the Aronimink Golf Course in Philadelphia.
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For Woods, his 62 was the second best opening-round score he's ever recorded. Woods wound up with a one-shot lead that day and tied for seventh.
Woods brought out of mothballs the old Scotty Cameron putter that he wielded in 13 of his 14 major championship victories, and it was just like old times as he putted with the assurance of yesteryear. His only bogey came at the par-3 eighth, by far the most hard pin on the course.
Woods is also first in strokes gained putting so far for the tournament.
After a 15-minute wait on the tee at the difficult par-3 No. 8-a 246-yarder that has played as the third-hardest par 3 on the PGA Tour since 2011-Woods tugged a 4-iron long and left, leading to an awkward chip and, eventually, his first bogey of the day. McIlroy drained an eight-foot birdie at the 18th, then holed three more putts between eight and nine feet consecutively as he made the turn.
"It's been something I've been struggling with all year and it's been much better the last couple of weeks", he said.
Two days after he was selected by Jim Furyk as a Ryder Cup captain's pick, Woods made a decision to put his trusty Scotty Cameron back in the bag after he'd employed two other Taylormade flatsticks in play recently.