He emulated the feat of compatriot Jesper Parnevik, who was second in the 1994 and 1997 Opens, but Sweden's long wait for a first major champion goes on.
"I felt the support from the Swedes and a lot of the crowds in general today," said Stenson who finished tied third in the 2008 and 2010 Opens.
"And of course I want to make it happen. But all you can do is ask to give yourself a chance and I did that."
Stenson rose to number four in the world in 2009, a year in which he won the prestigious Players Championship in Florida, but slipped back to 230th in the rankings before his recent return to form.
He won his first European Tour title for five years at the South African Open in November and has climbed back to number 30 in the world.
"I'm very pleased with my performance over the week and today more so than yesterday," Stenson told reporters.
"I thought I was in a good frame of mind and played some good golf. It was tougher out there today wind-wise and I got off to a great start.
"So I take a lot of positives and we'll be back trying again," added Stenson who also won the WGC-Accenture Match Play Championship in 2007.
The former Ryder Cup player said he had made improvements in his game this season but still lacked confidence in some areas.
He birdied two of the first three holes on Sunday, and picked up two more shots at the ninth and 17th, but bogeys on the eighth, 12th and 13th left him three shots adrift of champion Phil Mickelson.
"I've played this golf course very good," Stenson said. "Even though I made a few mistakes, I haven't made big mistakes that put me out of the tournament. Mentally, I've been in a good place all week.
"Experience is obviously a key factor and I've learned a lot this week. I'm ready to be back next year or at the U.S. PGA Championship next month and hopefully I can put myself in another good position."
(Editing by Tony Jimenez)
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