Rose’s fast finish closed out a six-under 65 at Pebble Beach and pulled the 2013 champion top of the congested leaderboard, where Rickie Fowler is among the four players sharing second spot.
Louis Oosthuizen, Xander Schauffele and Aaron Wise sit alongside Fowler on five under, while McIlroy is three strokes off the pace after an opening-round 68.
Two-time defending champion Brooks Koepka began his bid for a third consecutive US Open title with a two-under 69, with 15-time major champion Tiger Woods a further shot back.
Playing alongside Woods and Jordan Spieth, Rose made his move up the leaderboard after following a 15-foot birdie at the fourth with a 10-foot eagle at the par-five sixth.
Rose closed within one of the lead by holing a 15-footer at the seventh but bogeyed the next after failing to get up and down from just off the green, before ending a run of pars with a 10-foot birdie at the 16th.
The 38-year-old drained a 25-foot birdie putt at the par-three 17th to join the group tied at the top and then claimed the outright advantage by converting from 10 feet at the par-five last.
“Obviously a fun day of golf,” said Rose. “I guess the round was going nicely. I was three under par, had a rough patch, had to scramble, work hard and keep my round together.
“Even when I made a mistake, I was willing to accept [it]. 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.
“A great start to the week. [But] I wouldn’t say it’s exhilarating, because I feel like my mindset is I am in a 72-hole tournament. This is just a very small step towards outcome.
“So 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 damn, 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.”
Fowler had set the early clubhouse target, only for Oosthuizen to make a hole-out birdie from the bunker on the ninth – his final hole – and Schauffele to make a final-hole eagle to also get to five under.
Wise recovered from an opening-hole bogey to post six birdies and join the share of the lead, with Scott Piercy – who was five under after six holes – and Nate Lashley both sitting a shot off the pace.
McIlroy had posted opening rounds of 77 or worse in his past three US Open appearances but saw a big improvement by mixing four birdies with a sole blemish in a three-under 68, with Henrik Stenson and Francesco Molinari also three off the pace.
Koepka made the perfect start to his bid for a fifth major title by rolling in a 12-footer at the first, before following a birdie at the third with back-to-back gains from the fifth to get within one of the morning leaders.
The 29-year-old bogeyed the eighth after failing to get up and down from just off the green and then cancelled out a 20-foot birdie at the 12th with a blemish at the next.
Koepka missed a four-foot birdie chance at the 15th but drained a putt from double the distance to save par at the next, before bogeying the 17th and two-putting from four feet for a closing par to sit four strokes off the lead.
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