The peerless Woods won by a record 15 shots when the US Open was held at the picturesque Monterey venue in 2000, but the 43-year-old 2019 version ground out a one-under 70 to sit five off the lead of England's Justin Rose.
"It's typical Pebble Beach where the first seven holes you can get it going, and then after that you're kind of fighting and kind of hanging on," Woods told reporters afterwards.
"I had it going early and had to fight off through the middle part of the round and hung in there with pars. It's just fighting it out and grinding it out."
After four back operations, including spinal fusion surgery, Woods has to manage his body carefully, but he said the problem was his iron play on a short, tight course with small greens that demand strategy and accuracy above brute power.
"I didn't hit my irons as crisp as I'd like," said the world No. 5, who also won the US Open in 2002 and 2008.
"I tried to miss the ball in the correct spots, and a couple of times where I had wedges in my hand I was just dumping, center of the green, get my 30-, 40-footer and move on. I took my medicine when I was in a bad spot and just kind of grind it out."
Rose, playing alongside Woods, compiled a stunning 65 as he chases a second major title to add to his 2013 US Open triumph at Merion, Pennsylvania.
"This is just a very small step towards the outcome," said the 38-year-old. "You don't feel like that buzz that you would on a Sunday, but you can't help but look around over your shoulder, and [think] dam, this is Pebble Beach. Shot 65 and you're in the US Open. It's a cool moment. Whatever transpires the rest of the week, it was a cool moment."
The 29-year-old, bidding to become only the second player after Willie Anderson (1903-1905) to win three straight US Opens, carded a two-under 69 after escaping from a number of tricky spots including having to play his second off a concrete cart path on the 18th.
"I try to find some positive and try to spin it, even when something negative happens," said world No.1 Koepka, who has won four of his last eight majors.
One shot behind Rose was the quartet of Rickie Fowler, Xander Schauffele, Louis Oosthuizen and Aaron Wise.
"It was very stress free. It felt like the worst I could have shot," said world No.11 Fowler, who is still chasing his first major title.
Jordan Spieth, who won the last of his three majors at the Open in 2017, became the subject of much chatter on social media after he was heard to criticize caddie Michael Greller during the round.
The former world No.1, who is trending in the right direction after a mini slump of late, found the Pacific Ocean with his tee shot on the eighth hole before firing his third through the green.
"Two perfect shots, Michael," Spieth said to long-time caddie Greller. "You got me in the water on one and over the green on the other."
The pair are famous for their vocal discussions on the course, and Spieth regularly refers to himself as "we" when discussing his play, in a nod to Greller's input.
When he was quizzed about his comments afterward, Spieth told reporters: "When you hit a couple of shots exactly where you want to, and one's in the water and the other's dead over the green, I'm gonna be frustrated that, as a team, we didn't figure out how to make sure that didn't happen.
"I may have looked like the bad guy there but my intentions there were that we should have been in play if the ball is hit solidly and I was out of play on both shots."
When Spieth won the Open Championship at Royal Birkdale in 2017, he shouted to Greller: "Go get that," and pointed to the hole after sinking a 50-foot eagle putt on the 15th hole.
He later explained it had somehow lodged in his head after seeing loops of old Open footage while in the gym, in which caddies regularly fetched the ball from the hole.