Blixt, in only his second major tournament, and Stenson, coming off a runner-up effort last month at the British Open, each fired par-70s at Oak Hill in the final round of the $8 million event.
That left Stenson third on seven-under 273, three strokes behind US winner Jason Dufner and one stroke ahead of Blixt.
“I was still giving it a good fight and had an unbelievable round. I will take a lot of positives out of that,” Stenson said. “Happy with my performance. I kept it together nicely.”
Stenson opened with a bogey but answered with an eagle at the par-5 fourth.
“That put me back in a good momentum again,” he said. “I didn’t play best today but I was still hanging in there.”
After going bogey-birdie at the seventh and eighth, Stenson birdied the par-5 13th and matched runner-up Jim Furyk for second, two behind Dufner, but found a divot short of the green at 14 and made a rally-killing bogey.
“That killed the outside chances I had on the back nine to make a charge,” Stenson said. “Ended up plugging it in a bunker after duffing it in there.
“I can’t afford that at that time. If you are little behind and you need to make up some ground at these events, that could be make or break it.”
Blixt won last month at US PGA Greenbrier Classic to qualify for his first major, last month’s British Open at Muirfield, and the PGA Championship, where his third-round 66 put him in with a chance on Sunday.
A bogey-bogey start and finish spelled doom for Blixt’s title dream but he made four birdies on the back nine, including back-to-back birdies at 13 and 14 to leave him three back with four holes to play.
“Got myself in position to really attack the golf course and attack the lead. I was a little far back but you never know in a major what’s going to happen,” Blixt said.
“Coming down the stretch, got a little jittery again. Kind of exciting to be up there with those guys and seeing your name up there. I’ve got to get used to that a little more for next time.
“You get jittery. You get very excited. It’s a lot of fun to contend. But this is a new stage. I can probably handle this a little better next time.”
Blixt learned plenty about how he needs to handle the back-nine pressure in a major.
“I played well. I learned a lot, especially about myself and how I would react in a situation like this,” Blixt said. “I’m going to go back and analyze it a little more and see if I can do better next time. It was a learning experience and a lot of fun.”
Retired Swedish golfer and perhaps the county’s best-known male golfer Jesper Parnevik, who was ranked in the top ten for nearly 10 months in 2000 and 2001, won five PGA tournaments, but never claimed a major.