Rose's six-under-par 65 matched the American's record low round for a U.S. Open contested at the iconic seaside layout and gave the Briton a one-shot lead on a spectacular day of low scoring.
"Obviously a fun day of golf," said Rose, the 2013 U.S. Open champion. "I was three-under par, had a rough patch, had to scramble, work hard, keep my round together.
"I was trying to stay patient with myself mentally, but kept up-and-downing the ball, kept the momentum up.
"And then got rewarded with a hot finish, birdieing the last three, took a good round to a great round."
Woods flashed a familiar grimace during a sometimes torturous round on Thursday but it was his play that was proving troublesome, not his surgically repaired back.
The 43-year-old, who claimed his 15th major at the Masters in April, limited the damage from an early double-bogey by hitting back with two birdies and closing with 11 straight pars for a one-under 70.
The former world number one's start was a far cry from his opening to the 2000 tournament when he carded a 65 and romped to a record 15-shot victory.
It was good enough to keep him in contention, however.
"Well, it's just fighting it out and grinding it out," said Woods. "But I still say that it's important to miss the ball in the correct spots.
"Granted, I made a few putts today, but they were all uphill.
"Hitting the ball in the correct spots, if I happened to not feel comfortable with a number, dump the ball 30, 40 feet, move on about my business."
While Woods saw one of his longstanding marks equalled he has quite a few records within reach.
A win on Sunday would pull him even with Snead for the most career PGA Tour wins at 82 and he would join Nicklaus, Ben Hogan, Bobby Jones and Willie Anderson as winners of the most U.S. Open with four.
Perhaps most importantly, however, it would see him move another step closer to his Holy Grail, Nicklaus's record of 18 career major titles.
For the moment though the only thing on Woods's mind is the next round.
"It's a quick turnaround into tomorrow," said Woods. "Right away we've got a tough par four right from the get-go.
"And we have the harder side to start off on, and hopefully I can finish up on the front side and have the full seven holes where I can get it going."
(This story refiles to fix spelling to 'within' in first parragraph)
(Editing by Peter Rutherford)
