With his 1-over-par 281 total, Simpson, of Charlotte, N.C., became the ninth consecutive first-time winner of a major, and the 15th different winner in the last 15 majors.
Simpson, who was an Arnold Palmer scholar at Wake Forest, got some measure of satisfaction out of his win at Olympic. It was here in the 1966 Open that Palmer blew a 7-stroke lead with nine holes to play and lost in a playoff to Billy Casper.
Furyk, 42, who was born in West Chester and was seeking to add an Open title to the one he took in 2003 at Olympia Fields outside Chicago, didn't make a birdie the entire day. His worst swing of the round, a duck hook off the tee at the par-5 16th, led to a bogey that dropped him out of the lead.
Furyk was unable to make birdie at 17, another par 5, after putting his second shot in the bunker. Then, at the short par-4 18th, he knocked his second shot into the left greenside bunker and wound up with a bogey on the hole.
As Simpson watched the 18th in the scoring trailer with his wife, McDowell had a look at birdie from 24 feet out that would have pulled him into a tie, but he missed to the left, and Simpson and his wife celebrated.
Talking about his round, Simpson told NBC's Bob Costas: "It was a very nerve-racking day. I probably prayed more in the last three holes than I ever have in my life."
But Simpson was calm and cool under pressure. He knew what he had to accomplish to be the leader in the clubhouse and he did it, making pars on his final eight holes.
Michael Thompson, a second-year tour player who set the pace after the first round with a 66, roared back into contention with a 67 for a 282 and sat in the clubhouse for more than 90 minutes after finishing to see whether it would be good enough for a playoff.
That chance evaporated after Simpson sank a four-foot par putt at the 18th to close at 1 over.
Still, Thompson tied for second with McDowell, whose 73 featured three back-nine birdies.
Furyk shot a 74 to fall back into a four-way tie for fourth place with Padraig Harrington, David Toms, John Peterson, and Jason Dufner. Harrington and Toms had 68s, while Peterson and Dufner each matched par 70.
Tiger Woods, who began the day 5 strokes out, shot himself out of the championship on the first six holes, with four bogeys and a double bogey. He had a 73 for a 287 total, tying for 21st place.
Simpson, who is ranked 14th in the world, was 2 over for his round through five holes and 5 over for the championship before hitting his hot streak. He sank a seven-foot putt on the brutal 448-yard sixth hole to touch off a run of four birdies in a five-hole stretch. Birdies followed on Nos. 7, 8, and 10.
If you count his sand saves at the ninth and the 11th holes, Simpson had a streak of six one-putt greens.
Simpson could not convert birdie chances at the 15th and 17th holes. On 18, he pushed his second shot into deep rough to the right of the green but cozied his chip to four feet and made the putt.
"My hands were shaking, but at least it went in," he said.
Furyk played steady golf on the front nine with eight pars and a bogey and held a 1-stroke lead over Simpson at the turn. He sank his only putt of distance all day at the 12th, where he drained a 30-footer to save par and maintain his lead. But bogeys at 13 and 16 pushed him behind Simpson, and he could not recover.
Contact Joe Juliano at 215-854-4494 or firstname.lastname@example.org. Follow @joejulesinq on Twitter. Read his blog, Golf Inq, at www.philly.com/sports/golfinq