The 33-year-old American, who had forged three strokes ahead of the field with a 67 in the third round, held off a brave challenge from playing partner Stephen Leaney of Australia, finishing tied with the tournament record on eight-under 272.
One of the straightest hitters in the game, Furyk equalled the 72-hole mark first set by Jack Nicklaus at Baltusrol in 1980, and later matched by Lee Janzen at the same venue in 1993 and Tiger Woods at Pebble Beach in 2000.
"It's very special ... it's beyond some dreams," an emotional Furyk said.
"This is a heckuva present for Father's Day," he added, referring to his father Mike, who has been his sole swing coach since he turned professional in 1992.
Nineteen players had been under par going into the last day, but only four stayed there as the course firmed up and the greens became lightning fast under a baking sun.
Furyk struck a superb approach to within three feet of the flag for birdie at the par-four 14th to stretch his lead to four, and could afford to bogey the treacherous finishing holes at Olympia Fields Country Club to secure his major breakthrough.
He had wobbled briefly with his first dropped shots of the day on 10 and 12, and Leaney then closed the gap to three with a 40-foot birdie putt on 13.
But Furyk hit back immediately with his birdie on 14, and the end result, thereafter, was never in any doubt in bright afternoon sunshine.
The 34-year-old Leaney had provided a brave challenge, but experienced a roller-coaster round.
He started the day three strokes behind, but bogeys on one, three, seven, eight, 11 and 17 more than offset his birdies at the second, fourth, sixth and 13th.
"I'm happy and I'm sad," Leaney said.
"I thought I had a very big chance today, and even more so after holing that putt on 13.
"But Jim kept me at arm's length all day. It was disappointing but there are some good things to come out of this week."
Furyk, who possesses one of the most unorthodox swings in the game, played nerveless golf and had to sink two putts from 15 feet to salvage par in the first five holes.
Mike Weir, the U.S. Masters champion, had got to three under after 16 holes but dropped shots on 17 and 18 for a one-over-par 71, finishing in a tie for third with Kenny Perry at one-under 279.
Perry, winner of back-to-back titles on this year's PGA Tour, had earlier carded an impressive three-under-par 67 to hold the clubhouse lead.
"I played great today," the 42-year-old American said. "I hit a lot of fairways, a lot of greens and I could have actually shot four- or five-under."
Briton Justin Rose, in his first U.S. Open, carded a final-round 69 to tie for fifth at even-par 280 with twice champion Ernie Els (72), three-times major winner Nick Price (75), 2001 U.S. PGA champion David Toms (71) and Sweden's Fredrik Jacobson (71).
Defending champion Tiger Woods, whose title hopes all but disappeared with his third-round 75, was another to struggle after a promising two-birdie start.
His bid to vault up the last-day leaderboard was derailed by a four-putt double-bogey at the ninth, and he dropped two more shots on the back nine to finish with a two-over-par 72 at three-over 283.
"It's been frustrating the whole week," the world number one said. "I've not got anything going. I felt I was close to putting it together, but I need a bit of momentum."
Woods found the semi-rough at the 576-yard first after pulling his drive.
But, after hitting his second shot into the front left bunker, he splashed out to seven feet from where he made birdie.
Birdie number two came at the par-five sixth, when he rifled his approach to eight feet to move to two under for the day, where he remained following a regulation par at the 212-yard seventh.
At the par-four ninth, however, his approach screwed back to 30 feet below the hole.
With the greens quickening, his first putt shot past seven feet, he missed the putt for par coming back and another from four feet before finally holing out.
He never recovered after that and finished in a tie for 20th.