Stenson carded a closing 63 at Royal Troon to become only the second player to finish a major on 20 under par, equalling the record set by Jason Day in last year’s US PGA Championship.
As well as equalling the lowest score recorded in any major, which Mickelson had also done in the first round, it was only the second 63 in the final round of a major by the eventual winner after Johnny Miller in the 1973 US Open at Oakmont.
Stenson’s 72-hole total of 264 also eclipsed the previous best in a major set by David Toms in the 2001 US PGA and was three lower than the previous Open record set by Greg Norman at Sandwich in 1993.
“I felt like it was my time,” said the 40-year-old, who admitted time was running out after seven top-four major finishes.
“It’s not something you want to run around and shout, but I felt like this was going to be my turn. That was the extra self-belief that made me go all the way this week.
“It’s a dream come true. The Ryder Cup and the Open Championship were the big early memories I had so to sit here with this trophy is pretty amazing.”
Five-time major winner Mickelson, who had beaten Stenson into second place to lift the Claret Jug at Muirfield in 2013, found the positions reversed despite a flawless 65 to finish 17 under, with fellow American JB Holmes 11 shots further adrift in third.
“It’s probably the best I’ve played and not won,” said Mickelson, who at 46 was looking to become the fourth oldest major champion in history.
“I think that’s probably why it’s disappointing in that I don’t have a point where I can look back and say, ‘I should have done that’ or ‘had I only done this’.
“I played a bogey-free round of 65 on the final round of a major; usually that’s good enough to do it, and I got beat.”
Although the weather could not match the heatwave for the epic contest between Tom Watson and Jack Nicklaus at nearby Turnberry in 1977, the golf certainly revived memories of the ‘Duel in the Sun’ as the final pair combined for 14 birdies and an eagle.
Stenson had started the day with a one-shot lead, only to three-putt the opening hole from just short of the green after Mickelson had already fired his approach to within two feet.
The resulting birdie took Mickelson to the top of the leaderboard and he almost chipped in for another on the second, but it was Stenson who found the bottom of the cup from 15 feet to draw level. Another birdie from similar distance on the next restored Stenson’s overnight advantage, only for Mickelson to hole from eight feet for eagle on the fourth.
Stenson two-putted from long range there for his third straight birdie and the pair traded birdies on the par-5 sixth to remain tied for the lead, before world No 6 Stenson edged in front again with a birdie on the eighth.
Looking to become Sweden’s first male major champion, Stenson rolled in his sixth birdie in the space of nine holes on the 10th, but Mickelson crucially followed him in from eight feet.
The pair were tied for the lead again when Stenson three-putted the 11th, but for the third time this week Stenson birdied the par-3 14th and then struck the crucial blow on the next, holing from 50 feet from across the green to move two clear.
Mickelson was not about to throw in the towel and hit a superb approach to the par-5 16th, but after his eagle putt agonisingly slipped across the front of the hole, Stenson holed from four feet for birdie – having missed the green with his second – to remain two ahead with two to play.
A historic 62 was even on the cards after a superb tee shot on the 17th, but after missing the birdie attempt there, Stenson made no such mistake on the 18th to bring a fitting end to an astonishing day.
“It hasn’t quite sunk in yet but I’m very happy,” the Ryder Cup star added. “I’m very proud of the way I played. It was a great match with Phil. I knew he wasn’t going to back down at any point, and in a way that makes it easier for myself.
“I knew I had to keep on pushing, keep on giving myself birdie chances and he wasn’t going to give it to me, so I had to pull away. I’m just delighted I managed to do that with a couple of birdies at the right time on the final stretch.”