Clark, whose previous best finish in six prior major starts was a tie for 75th, shrugged off two late bogeys to close with a pair of confident pars for an even-par 70 to seal victory with a 10-under-par total of 270 at Los Angeles Country Club.
That was good enough for a one-shot win over McIlroy, who also closed with a 70. World number one Scottie Scheffler carded an even-par final round to finish third on 273.
Clark dedicated his Father's Day victory to his late mother, who died from breast cancer in 2013.
"I just felt like my mum was watching over me today. She can't be here. I miss you, mum," said Clark, who had broken through for his first US PGA Tour victory at Quail Hollow just last month. "I just feel like it was my time."
Clark, ranked 32nd in the world, started the day tied for the lead with Rickie Fowler and had a three-shot lead after his fourth birdie of the day at the par-five 14th where he reached the green in two and two-putted for birdie from 20 feet.
McIlroy, playing a group ahead, had bogeyed the same hole.
But Clark's lead dwindled to one after bogeys at 15 and 16, and McIlroy kept the pressure on with an unlikely par at 17 -- where his errant tee shot ended up on the fairway of the neighbouring second hole.
Clark missed the green at the par-four 17th but stuck his third shot within two feet of the pin for a needed par.
His approach at 18 left him 60 feet from the hole, and he made a confident run with his first putt and sealed the victory with a par putt from within three feet.
"I hit some great shots coming down at the end, and although I made a couple of bogeys and it seemed like maybe the rails were coming off, I was inside pretty calm," Clark said. "I'm really pleased with myself with how I performed."
McIlroy had opened with a birdie, then parred 12 straight, finding green after green but unable to get any birdie putts to drop.
He bogeyed 14, where his third shot was plugged deep in the muddy bank of a bunker and he received a free drop, only to miss a nine-foot par-saving putt.
"I hung in there and fought right to the end and didn't quite get the job done," said McIlroy, who won the last of his four majors in 2014. "But I'll keep coming back until I get another one."
'I can do this'
Reigning British Open champion Cameron Smith of Australia climbed the leaderboard with a 67 to grab fourth place on six-under 274.
Fowler, trying to claim his first major title to cement his return from a slump that saw him fall to 185th in the world, endured a nightmare day with seven bogeys in a five-over 75.
It was a disappointing end to a week that saw him break the US Open record for a low round with a 62 on Thursday.
Fowler ended up sharing fifth with Australian Min Woo Lee and Tommy Fleetwood -- who carded a superb seven-under-par 63 to become the first golfer with two rounds of 63 on his US Open resume.
Clark opened with a birdie, but immediately gave a shot back at the second hole. He rolled in a five-footer for birdie at the par-three fourth and had a two-shot lead after a birdie at the sixth.
He gave a stroke back at the par-five eighth, where he found himself hitting out of waist-high clumps of grass left of the green.
His first attempt to hit out barely advanced the ball and his next went through the green.
He limited the damage with a chip to three feet on the way to a bogey that put him at 11-under.
"That was a huge point in the round," Clark said.
Clark drained a seven-foot putt to salvage par at the par-three ninth after hitting his tee shot into the rough on the edge of a greenside bunker.
"US Opens are tough," Clark said. "It's tough on the back nine trying to win a tournament. I felt at ease and I just kept saying 'All right, I can do this, I can do this.'"
