Mickelson started the day five shots behind overnight leader Lee Westwood. But as the Englishman started to falter it was the American who managed to find some birdies in the closing holes.
Westwood, who was chasing his first major championship, never really got going on Sunday, allowing an uncharacteristic lack of judgement around the tricky Muirfield set up, slipping back into third place with a final round 75.
Dropped shots at seven and eight, saw the 40-year-old tied for the lead through nine holes, with Stenson and Australian Adam Scott.
Scott took the outright lead with a birdie on 11, but the 32-year-old couldn't become the first player to win both the Masters and the Open in the same year since Tiger Woods in 2005.
Four bogeys in a row from the 13th effectively ended the Australian's charge as Mickelson posted four birdies in his final six holes to post an insurmountable clubhouse lead at three-under-par.
"It's probably the greatest and most difficult win of my career. It is great to be part of any Open Championship and to win at Muirfield feels amazing," Mickelson said.
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