Up next is the final major golf tournament of the year with the PGA Championship held at Baltusrol Golf Club in Springfield, New Jersey.
Mickelson, who had beaten Stenson into second place to lift the Claret Jug at Muirfield in 2013, had to settle for second place on 17 under despite a flawless final round of 65, with American JB Holmes an fantastic 11 shots further adrift in third.
Troon. - Henrik Stenson emerged victorious from a titanic duel with Phil Mickelson to win the 145th Open Championship at Royal Troon yesterday after firing a final round of 63 that equalled the lowest round score in major history.
For Stenson, it was his first major championship win at the age of 40.
Mickelson, 46, the San Diegan who has five major championships, was denied despite scoring 65, his lowest final round ever in a major. But on this Sunday, it was Stenson's time.
Stenson joined Johnny Miller as the only player to shoot a 63 in the final round of a major.
Records didn't matter. This was about winning his first major. "The way I was able to hit fairways easily coming down the stretch and hit my iron shots right on line, draws and fades and so forth, and basically that comes from getting my swing back on plane". He has now finished in the top 10 in eight of the last 11 major tournaments he has competed in.
Later he added: "He was one of the real good guys back in Dubai".
"I'd love to play the final round the way I did the first two and give myself a shot", he admitted. "I'm happy with the way I played, but even more disappointed that it wasn't enough because you look back and say, 'what do I need to do?'"
"I played what I feel was well enough to win this championship by a number of strokes and yet I got beat by three strokes. And I got beat".
The 22-year-old Texan had gone 10 straight rounds in major championships without breaking par.
Stenson's final score broke Greg Norman's record for the lowest four-day total in an Open and tied Jason Day's mark for the lowest score in relation to par in a major championship. This time, it was a birdie that clinched his first major and made a little bit of history along the way. "It could have been a day that got away from me, so I'm proud of that". I'm happy with where my game has come this year.
The pair put on a sublime masterclass of skill and nerve despite the testing, breezy conditions in a showdown which will arguably eclipse the famous "Duel in the Sun" Open when Tom Watson beat Jack Nicklaus in an epic battle at Turnberry in 1977.
Mickelson was not about to throw in the towel and hit a superb approach to the par-five 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. Together, they have combined for seven birdies, one eagle and just one bogey. Over the last two days, they've never been more than two shots apart. "I knew I was going to have to battle back if it wasn't, but I think that was the extra self-belief that made me go all the way this week".