Fresh from his victory at last week's RBC Canadian Open, the Northern Irishman fired four birdies before a closing bogey meant he had to settle for a share of second place on three under par, one shot behind Canadian Hadwin.
A brilliant birdie blitz on the front nine helped afternoon starter Hadwin produce an opening 66 to lead the way at The Country Club.
McIlroy was joined in a tie for second by Callum Tarren, David Lingmerth, Joel Dahmen and MJ Daffue, with Matt Fitzpatrick and Justin Rose among those another shot further back.
Starting from the tenth tee, World Number Three McIlroy opened his round with six straight pars before picking up his first birdie from 20 feet at the short 16th.
A sensational approach into the 17th green set up another birdie chance but his seven-foot effort slid just by.
McIlroy did not have to wait long for his second birdie of the day, though, guiding home his 17-foot putt at the 18th to reach the turn in 33.
The 33-year-old started his back nine with another run of six straight pars, which featured an impressive save at the fifth.
Having broken that run with a monster birdie putt on the seventh, McIlroy also birdied the eighth to jump to four under.
But after missing the green with his approach at the ninth, he finished with a bogey to complete a 67.
Just under a month on from his opening 65 at the US PGA Championship, McIlroy was pleased with his start here.
The 2011 U.S. Open winner said: "You'd take 67 around this golf course any day. Even though I'm standing up here slightly frustrated that I bogeyed the last, it's a great start to the tournament.
"I felt like I did most things well today. I certainly putted well, and I hit the ball in the right spots, and I hit a lot of greens, gave myself plenty of chances. Just basically did everything that you need to do at a U.S. Open.
"Overall I'm really pleased about the start. That's now two Majors in a row that I've started well, and hopefully just keep going from here."
Five birdies in six holes from the fourth helped Hadwin banish the memory of his bogey at the third as he got to the turn in 31 shots.
And although he dropped another shot at the 12th, Hadwin got it right back on the 13th with an enormous birdie putt.
He said: "Not much better of a start to a U.S. Open I don't think that you can ask for. I did a lot of good things.
"I got a nice run there midway through the front. I do think there's a few more scorable holes as long as you hit good quality golf shots there.
"Then I kind of just held down the fort there the last little bit. Some key up-and-downs. Made a nice one from the fringe on 13. Just doing a lot of good things.
"I hit the ball really well the last four holes, which I was really pleased with. I kind of found a little something there at the end.
"We'll try again tomorrow."