Rose, who won his only major at the 2013 US Open, carded a six-under-par 65 at Pebble Beach, California.
Four players are tied for second, with Americans Rickie Fowler, Xander Schauffele and Aaron Wise alongside South Africa's Louis Oostuizen.
Rory McIlroy is on three under with Brooks Koepka a shot back and three-time champion Tiger Woods on one under.
World number one Koepka is trying to become the second man to win three successive US Open titles - after Scotland's Willie Anderson (1903-05) - and got his defence off to a lightning start with four birdies in his opening six holes to move within one stroke of the early clubhouse leaders.
But the 29-year-old American, who won the US PGA Championship last month, bogeyed the eighth and then saw a birdie at the 12th immediately wiped out as he struggled with his driver and approach play on the back nine, carding another bogey at 17 to finish on two under.
However, he putted well and said: "I felt the most comfortable on the greens this week of all the majors we've played so far.
"I feel like I'm putting great and the greens held up really well."
Scores were unusually low for a US Open, with 57 of the 156 players in the field finishing on level par or better.
Record start for Rose
World number four Rose, 38, birdied the fourth and then eagled the par-five sixth before holing another birdie on the seventh to get to four under par.
The only blemish on his card was a bogey on the eighth but he followed that with seven pars before his closing birdie run to complete the joint-lowest score at Pebble Beach in the US Open.
That record had been held by his playing partner Tiger Woods, when he won the first of his three US Open titles by 15 shots in 2000.
"I wouldn't say inspired but I was aware of it and on the last hole for sure," said Rose, who had 14 one-putts and just 22 putts in total.
"I was grinding, trying to get off to a good solid score. I was watching the television coverage in the morning and I heard that 65 was the best score and there are some things you can't unhear.
"It was nice to do it in front of the man himself."
He added: "I don't think we've seen the course under US Open conditions yet. The breeze was just benign enough. I believe it could be more windy on Friday so I'm glad I got off to a good score when it was gettable."
An agitated Woods found himself continuously scrambling to save par, including a wonderful 30-foot putt at the 15th - one of 11 straight pars from the eighth for the Masters champion.
They came after a run of three birdies and a double bogey - his only dropped shots came after a wild tee shot at the par-three fifth.
The long-time clubhouse leaders
Fowler has enjoyed eight top-five finishes but is yet to win a major title. He had just one bogey on his way to a five-under-par 66 on Thursday.
"I said earlier in the week that whether I win a major or I don't in my career, it's not something that's going to define me," said the American.
"There's a lot of other things that I'd love to be remembered by, work off the golf course and making a difference and changing people's lives. It would be nice to have a major on the resume. We'll see what we can do."
Oosthuizen, runner-up in 2015, made three birdies on his back nine while 22-year-old Wise - tipped by practice partner Koepka before the tournament to be a future star - did not drop a shot after bogeying his opening hole.
Meanwhile, Schauffele eagled the last to take his place among the clubhouse leaders before Rose's late flourish.
McIlroy makes fast start
Rory McIlroy has won four majors, including the 2011 US Open
McIlroy sits three shots back after the 2011 champion recovered from a bogey on his opening hole to finish with a 68.
The Northern Irishman has carded opening rounds in the 60s in all four of his major victories, going on to win the 2011 US Open by eight strokes at Congressional, but the last of those wins came five years ago.
The world number three was among the early starters on the 10th tee and he made the most of benign conditions as he brushed off a dropped shot at his first hole to birdie the 13th and par-three 17th, as well as scrambling for par at 18, to hit the turn at one under.
McIlroy then holed from 12 feet for his third birdie of the day at the second and immediately backed it up with another to move to three under.
He said he was "really pleased" to open with a 68 after posting rounds of 65, 67, 66 and 66 when he won the 2011 US Open, 2012 US PGA Championship, 2014 Open Championship and 2014 US PGA.
"I did what I wanted to do, which was hit it in the fairways for the most part, hit a lot of greens and when I didn't I was able to get it up and down," he said.
"I did everything you need to do in a US Open, I stayed patient after I bogeyed the first and played really solid after that so I did what you are supposed to do, make a lot of pars, chip off the birdies when you can and it was a good day's work."
Northern Ireland's Graeme McDowell, who won the US Open the last time it was staged at Pebble Beach in 2010, was the only one of the early starters to post a bogey-free round and sits on two under alongside Matthew Fitzpatrick, who is one stroke clear of fellow Englishmen Paul Casey, Matt Wallace and Tyrrell Hatton.
Hatton, who recorded his best finish at a US Open when he finished joint sixth last year, climbed to four under without dropping a shot in his first 15 holes, but finished with three bogeys.
A shot further back on level par are Tommy Fleetwood, who finished with two bogeys, and Danny Willett. Americans Phil Mickelson and Jordan Spieth are one over.
Henrik Stenson finished strongly, with the Swede making four consecutive birdies from the fifth to post a 68, the same as Open champion Francesco Molinari, who birdied the last.
South African-born Rory Sabbatini, who now represents Slovakia, grabbed a hole-in-one at the 202-yard par-three 12th, cheering ecstatically as his bright yellow ball bounced twice before disappearing into the cup.
"I told my caddie we've been having a lot of close calls and one is going to go in sooner or later, but I wasn't expecting that," said Sabbatini, who finished at one over.