Stenson shot an 8-under 63 on Sunday to finish the tournament at 20-under and claim his first major championship. He won Sunday's matchup with Mickelson by 2 strokes and the Claret Jug by 3 over the American.
Stenson's final stroke of this major masterpiece was a 20-foot birdie putt on the 18th hole at Royal Troon that tumbled into the cup on the final turn. His 63 matched Johnny Miller for the lowest closing round by a major champion.
Both Stenson and Mickelson played stellar golf, combining for an eagle, 14 birdies and two bogeys in the final pairing.
"Thank you very much for a great fight," Stenson told Mickelson as he accepted the Claret Jug.
J.B. Holmes finished third. He was 14 shots behind.
Stenson delivered a crushing blow to Mickelson's chances of capturing a sixth major championship by making a 50-foot birdie putt from off the green at No. 15 that gave him a 2-shot lead with three to play. It was the first time all day the final group had been separated by more than 1 stroke.
The 40-year-old Stenson started walking when the putt was halfway there, stopping to pump his fist, rare emotion for the Swede with ice-blue eyes.
Mickelson narrowly missed an eagle putt on the 16th hole, and Stenson kept his 2-shot lead with an up-and-down for birdie from the deep rough.
Stenson's previous best finish in a major was a tie for second at the 2013 Open at Muirfield, which Mickelson won. Stenson becomes the first male Swedish golfer to win a major.
His total of 264 set a record for lowest score at a major. Stenson eclipsed the Open mark of 267 set by Greg Norman at Royal St. George's in 1993 and the overall mark of 265 by David Toms at the 2001 PGA Championship.
For Mickelson, it's an 11th runner-up finish at a major in his career. Only Jack Nicklaus, with 19, has more second-place results.
"I threw as much at him as I could, and he didn't make any mistakes," Mickelson said of Stenson on the NBC broadcast. "... I'm happy with where my game has come this year. I just haven't gotten the win yet."
The Associated Press contributed to this report.