Clark, whose other major crown came at the 2023 US Open, fired a three-over par 73 to finish 72 holes on four-under 276 and defeat fellow American Burns by one stroke.
Clark began the day with a six-shot lead, saw it shrink to a single stroke as he struggled early, then grinded through the back nine,
He did not secure victory until a tap-in par at the last hole, celebrating on Father’s Day with a hug from his dad Randall, who flew in to surprise him after the win.
Clark captured the record top prize of US$4.5 million from a US$22.5 million purse, but the effort had greater meaning as well.
The 32-year-old American said it was a way to help him erase the bad feelings over smashing a locker at Oakmont after missing the cut in last year’s US Open.
Clark also became only the ninth wire-to-wire US Open winner and the first since Germany’s Martin Kaymer at Pinehurst in 2014.
Burns was second on 277 after a closing 67 with South Korean Tom Kim third on 279 after a 70.
Top-ranked Scottie Scheffler fired a 71 to share fourth on 280 with fellow Americans Keith Mitchell and JT Poston.
Scheffler, a four-time major winner, would have completed a career Grand Slam with a victory on his 30th birthday.
Greg Norman at the 1996 Masters was the only golfer to ever lose a major after leading by six or more through 54 holes, but Clark made things tense for a while.
Clark, who won his fourth PGA Tour title last month in Texas, made bogey at the par-three second hole while Burns birdied three of the first five holes.
His approach at one landed inches from the hole to set up a tap-in birdie. Burns added a birdie putt from just inside eight feet at the third and sank a 26-foot birdie putt at the fifth.
Clark sank a 15-foot putt to save par at the fourth, but Burns responded by sinking a birdie putt from just inside 50 feet at the eighth.
When Clark missed a 24-foot par putt at the par-five fifth, his bogey trimmed the lead to one shot.
Burns missed the green on his approach and made bogey at nine but Clark missed a four-foot par putt at the par-three seventh and the lead was again one.
A 78-foot chip to within inches of the hole saved par at nine to keep Clark ahead and he followed with a four-foot par putt at 10 to boost his lead.
Burns fell three adrift with a three-putt bogey at 15, but Clark missed an eight-foot par putt to bogey 13 and Burns sank a 17-foot birdie putt at the par-five 16th to pull within one again.
Tension built with the outcome on a knife’s edge as Burns barely missed a 16-foot birdie putt at 18, the result bringing him to his knees.
Clark found deep left rough off the 16th tee but blasted into the fairway and sank a dramatic 24-foot birdie putt for a two-stroke lead.
Clark, however, missed a six-foot par putt at the par-three 17th and his lead was again one.
At 18, Clark needed to two-putt from 52 feet for the victory. His first stopped inches from the hole and he tapped in for victory.
Burns, 29, failed to grab a first major title and first victory in more than three years. (AFP)