In becoming the first Swedish male golfer to win a major championship, Henrik Stenson did so with a style that no catwalk could better. He had a final round at Royal Troon of 63, eight under par and including two bogeys, for a 20-under-par total of 264, the lowest 72-hole score in any major and equalling the most shots below par ever in a major. His 63 may be the greatest single round of golf ever played. The only the man to win a major by shooting that low in the final round was the first to do it, Johnny Miller at the 1973 US Open, and he began six shots off the pace, without the incessant pressure of knowing he was in contention.

Stenson’s playing partner, Phil Mickelson, shot a bogey-free 65, which in any version of common sense he must have expected would win him his second Open and his sixth major. Aged 46, Phil was bidding to become the oldest man to win the Open since Old Tom Morris in 1867. His last tournament victory had been the 2013 Open at Muirfield, when Stenson finished second, the year the Swede topped the money lists on both sides of the Atlantic.

This was glorious golf. Seldom can greatness have looked so straightforward, which is mostly where Henrik hit the ball, just as his coach, Pete Cowen, has taught him. The final round had begun with Stenson, on 12 under par, leading Mickelson by a stroke and third-placed Bill Haas by six. Even Nick Faldo, who knows a thing or two about winning major championships from six shots back, had said on Sky the previous evening that he saw this as a two-horse race. Indeed it was.

In some ways it was a reprise of the famous 1977 Tom Watson/Jack Nicklaus ‘Duel in the Sun’, albeit with much less sun. Then Watson had prevailed by a stroke and Hubert Green had finished third, 11 shots adrift of the champion. At Troon, Stenson won by three – though it never felt that easy –  and the third-place man, J.B. Holmes, was 14 away. The two chief protagonists had almost lapped the field.

Teeing off at 7.40, almost seven hours ahead of the leader, the first player to hit a shot in anger on Sunday was Colin Montgomerie. (How many times during his career has Monty seemed to be hitting shots in anger?) This was because he was the last man of those left standing after a third-round 79. Coincidentally, this honorary son of Troon – his dad used to be the club secretary – had been the first man out on Thursday, when he opened with a double-bogey six. He did the hole in two shots less this time around and he managed to avoid continuing the pattern whereby his rounds had been getting four shots worse by the day. He shot 76 and thus also avoided finishing last.

Out several hours after Monty on Thursday, Mickelson had returned a 63, so nearly a 62. It was the ninth-ever 63 at the Open and the 28th in a major. (Greg Norman and Vijay Singh have done the trick twice.) He had an 18-footer for a closing birdie and a cherished place in history. It looked in all the way – until it somehow wasn’t. “I feel like crying,” he said, unconsoled at having a three-shot lead over Martin Kaymer and Patrick Reed. “I don’t know how that putt stayed out. It was an opportunity to do something historical and with a foot to go I thought I had done it. It was just heartbreaking.”

After a second-round 69, he still had the lead on Friday night, although now by a solitary shot from Stenson, who had fired a 65. “I’m 40,” said the Swede.” I’m not going to be playing in these tournaments forever. I don’t have another 50 goes at them…so I better start putting myself in position and giving myself chances if I want to make it happen.”

His 68 on Saturday, to Mickelson’s 70, gave him the opportunity to do that. It is fair to say that he stepped up to the plate. By Saturday evening he had sneaked into a narrow lead, not least thanks to making birdies at the two par-threes on the back nine, the 14th and 17th, while Mickelson bogeyed them. On Sunday, they both played golf from the gods. On the front nine, Henrik retaliated to the disappointment of an opening bogey with birdies at 2, 3, 4, 6 and 8. Phil matched his outward 32 with two birdies and an eagle. They both birdied the 10th but when Stenson three-putted 11, they were tied again, as they were until the 14th, where Stenson knocked in a 15-footer for a two.

At the 15th at Turnberry in 1977, Watson had holed a crucial and unlikely birdie putt from around 50 feet. Stenson did that here. He was two clear. They both birdied the par-five 16th, Mickelson made a trademark preposterous up-and-down par on 17 (where Stenson missed from eight feet for another two), and after Phil had two-putted for his par at the last, Stenson knocked in a 20-footer when he had three putts to win the claret jug. Like I said, it was the most simple-looking 63 you could ever see.

“I felt it was my time,” said Stenson. “I feel very privileged to be the one with this trophy. So many great Swedish players have tried and there have been so many close calls.” For his part, Mickelson said: “That is the best I have ever played and not won. I knew that Henrik would ultimately come through and win [a major one day]. I’m happy that he did. I’m disappointed that it was at my expense.”

Stenson, of course, will be in the European team for the Ryder Cup match at the end of September. So will Europe’s official leading player, Rory McIlroy, who had rounds of 69-71-73-67 (like Monty, he avoided recording an unwanted mathematical regression) to finish fifth, tied with Tyrrell Hatton to be low Brits. Like Jason Day, Dustin Johnson and Jordan Spieth, his fellow-members of the world’s top-4, and unlike Stenson (who is now ranked fifth) and Mickelson, McIlroy had got the worse side of the draw for the first two rounds. “It’s the Open Championship,” he said phlegmatically. “Some draws go your way and some don’t. The last Open I played [that was in 2014; he was injured last year] I got the good end of the draw and good things happened.”

Rory won at Hoylake that week and for sure he’ll be back again, chasing down a fifth major. Henrik, meanwhile, is happy to have his first, this after shooting the tenth 63 at the Open. (Did I mention it included two bogeys?) As for Phil, his marvellous effort in Ayrshire will serve to have even more people rooting for him to win a US Open and complete his personal Grand Slam. He would have been a hugely worthy winer at Troon but he was unlucky that one guy, and only one guy, deserved it more.

Robert Green’s ‘Seve: Golf’s Flawed Genius’ is available on Amazon. You can follow him on Twitter @robrtgreen