Stenson shot an 8-under 63 to finish the tournament at 20-under. He won Sunday's matchup with Mickelson by 2 strokes and the Claret Jug by 3 over the American.
Both played stellar golf, combining for an eagle, 14 birdies and two bogeys in the final pairing.
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.
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 score of 264 broke the Open scoring record. Stenson eclipsed the mark of 267 set by Greg Norman in 1993.
The Associated Press contributed to this report.