In his last three tournaments Stenson has two runner-ups and a third.
Jonas Blixt, another Swede, also had a 70 and finished fourth.
Masters champion Adam Scott never made a serious move and shot 70 to tie for fifth. Defending champion Rory McIlroy made triple-bogey on the fifth to lose hope, though he still closed with a 70 and tied for eighth, his first top 10 in a major this year.
Dufner two-putted for bogey on the 18th from about 10 feet and shook hands with Furyk as if he had just completed a business deal. He hugged his wife, Amanda, and gave her a love tap on the bottom with the cameras rolling.
Asked if he had ever been nervous, she replied: “If he has been, he’s never told me.”
That is what gives Dufner is own personality on the PGA Tour. He did not look any differently on the opening tee shot than when he stood on the 18th hole.
“I would say I was pretty flat-lined for most of the day,” he said.
Dufner became the sixth player to win a major with a round of 63, joining Tiger Woods, Greg Norman, Raymond Floyd, Nicklaus and Johnny Miller.
He is the third first-time major champion of the year and the 15th champion in the past 19 majors who had never won the big one.
Woods is responsible for the trend, mainly because he is not winning them at the rate he once was.
Woods extended his drought to 18 majors without winning and this time he was not even in the hunt. For the second straight round, Woods finished before the leaders even teed off. He closed with a 70 to tie for 40th, 14 shots off the lead.
“I didn’t give myself many looks and certainly didn’t hit the ball good enough to be in it,” Woods said.