Super composed, Scott rebounded from a first-hole bogey with four birdies, including three on the back nine, in a stylish Saturday three-under-par 67 at the fearsome Oakmont Country Club.
Australia's former world No.1 is only the third player in US Open history to start with three rounds of 70 or better at the tournament's most demanding layout.
Curtis Strange achieved the feat in 1994 before Shane Lowry matched the record eight years ago.
Scott's 70-70-67 start leaves the 2013 Masters champion just one stroke behind American leader Sam Burns, who carded a one-under 69.
Fellow American JJ Spaun bogeyed the last hole in a round of 70 to join Scott at three under.
For much of the day, Scott hovered at even par before exploding with three birdies in the last six holes on 13, 14 and 17.
At 44, Scott is bidding to become the second-oldest US Open winner of since Hale Irwin in 1990.
Victory would also place the Australian in the history books for the longest wait by a player between their first and second major championship triumph.
"At this point, it's just all opportunity for me. I feel like there's all upside," Scott said.
"I'm lucky. I've won a major. I'd love to win the US Open tomorrow. It's going to take a really great round of golf, something like what I did today, I believe, and fortunately the confidence is up so I should take advantage of it."
And golf's most likeable elder statesman has experience on his side, with Scott the only major winner sitting inside the top 10 entering Sunday's final round (Monday AEST).
Contesting an extraordinary 96th consecutive major, Scott three-putted the opening hole in a deflating start.
But the veteran put the hiccup behind him to collect his first birdie of the day at the par-5 fourth hole.
Then he hit the go button down the stretch to be well-poised to break a five-year winless run since taking out the Genesis Invitational in Los Angeles in 2020.
"I played really solid today," Scott said.
"Conditions were a lot softer, but there's still plenty of trouble to get in, and I drove it well off the tee. I was in most fairways, I would say.
"And the couple of times I missed, I managed to escape. So it was a good solid US Open round of golf."
Norwegian Victor Hovland is outright fourth at one under after also shooting 70.
The quartet are the only players in red numbers.
Playing his first major since 2022, Monday qualifier Marc Leishman rocketed up the leaderboard with a birdie-filled round of 68 to be tied for 11th.
But the revitalised Australian looks a little too far back at four over and eight shots adrift of Burns, as is world No.1 Scottie Scheffler who could only manage an even-par third round after a wretched day on the greens.
Jason Day (72) is one shot further back in equal 21st.
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