Phil Mickelson equalled the record low round in an Open Championship – and in all Majors – at Royal Troon overnight with an incredible 8-under par 63, but it might so easily have been one better.

A lip-out birdie putt from 6 metres at the 18th hole, the ball touching the right edge of the cup and refusing to co-operate, cheated him of a monumental piece of history.

“I wanna cry,” were the words he used to start his media conference, and that summed it up.

In all the 156 years of the Open, and all the years of men’s major championships, nobody has managed to shoot 62. Twenty-seven before Mickelson today had managed 63, and eight in the Open Championship. But none has gone lower, which explained why a man with a three-shot lead in the Open could be so disappointed.

“It really stings to have a chance,” he said.

“It’s such a rare opportunity to do something historic like that and to … I mean, if I had just hit a weak flail-off and never had a chance and left it short, so be it. But this ball was hunting right in the centre and didn’t go. It was just heartbreaking.”

Mickelson, the 46-year-old veteran, conjured some of the best golf of his storied career in the late afternoon and early evening, and when his birdie putt at the par-three 17th hole curled over the front edge of the cup, he was eight-under.

Everyone with a knowledge of golf, including Mickelson, would have been aware of what this meant.

After the American hit his 6-iron second shot on 18 to the green and into birdie range, Ernie Els, playing alongside him, asked if he knew. Of course, he did, and Mickelson told his caddie Jim “Bones” Mackay he needed his best read on the putt, a right-to-left slider.

Els, the generous man with the sense of history, offered to putt first even though he was nearer the hole, just to set the scene. In stepped ‘Lefty’, feeling focused, reading the line as just outside the cup on the right side. He stroked it nicely, watched it ease down as it reached the hole, then spin off the right lip and out. Mickelson put a hand to his face.

Later, he said the disappointment came from knowing that in all likelihood, he will never get another chance.

It was America’s day at Troon again, although no one can quite explain the quirky dominance of US golfers at the course where the past six Open winners all came from across the Atlantic. For a long time Patrick Reed (66) held the lead, after Justin Thomas (67) had taken originally set the clubhouse mark. Late in the day, Germany’s Martin Kaymer matched Reed’s 66 to put a slightly European slant on the leaderboard.

But Mickelson did not make a single bogey in a round that he rated one of his best, though not in the same class as his final round at Muirfield in 2013 when he won his only Open to date.

He joked that there must be some kind of curse on players who threaten to shoot 62.

“Well, it was obvious right there, there’s a curse because that ball should have been in,” he said.

“If there wasn’t a curse, that ball would have been in and I would have had that 62!”

A reporter asked: “Do you believe in the golf gods?”

Mickelson replied: “I didn’t, but I do now!”

It was a truly remarkable day.