On a warm, rainy night in 1974 Muhammad Ali changed the world in the moment it took a gloved fist to swivel the previously impenetrable jaw of big George Foreman. The location of the contest was as improbable as the result, a jungle clearing in the former Zaire, a stone’s throw from the Congo River, crocodiles looking on as the world’s television crews jockeyed to record what continues to be regarded as the greatest sporting event of all time.

On Sunday on a small strip of links land on the West Coast of Scotland, with television commentators conspicuously struggling to find the words to relate the magnitude of what they were watching, with fans and viewers rubbing their eyes and pinching their arms, with me begging my sister to put back our restaurant booking by another hour, Tom Watson came within a hair’s breadth of creating a story to rival what occurred on that startling night in Africa.

The American golfer was not merely battling younger, fitter, opponents as he made his way around the ancient course at Turnberry, he was vying with the ageing process itself. With mortality. With the Grim Reaper, scythe, cloak and all. For two hours on the inward nine, the 59-year-old, six weeks from his 60th birthday, more than three decades after winning his first Open title, looked as if he was going to subvert everything that we thought we knew about sport, about life.

His hitting was straight and clean, his strategy enlightened, his stroke-making flawless even as his joints were creaking. This was a man with a plastic hip, more wrinkles than a prune, and yet he had the glorious, thrilling, subversive impudence to believe that he could win the biggest prize in golf. Ultimately, he failed, an 8ft putt for the championship on the 72nd hole leaking to the right, but he had nonetheless succeeded in turning the world on its axis.

Competitive sport — at least at its highest level — is not supposed to be a place for the old or even the middle aged. I got out of international table tennis at the age of 32, not because I had lost the will or the desire, but because I couldn’t get my body to do the things that I asked of it. It wasn’t just that I was slower, a millisecond off the pace, but that I had lost the precision, the subtlety and the accuracy that ultimately separates the best from the rest. My opponents pounced like hyenas on a carcass.

At Turnberry on Thursday, 156 competitors took to the field, the vast majority in their twenties and thirties. Hyenas all. Voracious and motivated. Enough ambition to power a small town for a week. There was also a sprinkling of competitors in their forties and fifties. And then there was Watson, the oldest of all by more than six years, there by dint of the curious rule that permits former champions to keep coming back until the age of 60, providing fans with the opportunity to salute the heroes of the past as they totter around the old course.

But Watson was not there for a ceremonial, he was not there for a regal wave or two, he was there to win the damn thing. The very fact that he dared to believe was thrilling enough, but to have held his game together as the pressure mounted — cumulatively, irresistibly, intolerably — over the final two days was more than heroic, it was revolutionary.

It spoke of indomitability and courage. It spoke of audacity. Most of all, it spoke of the curious things that can happen when we believe in the impossible. And for a few heady moments, Watson made believers of us all.

Some will argue that our admiration for Watson should be tempered by recognition that golf is a sport that suits the older man. But this is to misconstrue the thing. Had Watson triumphed, he would have been more than 13 years older than any previous winner in the 150-year history of the event, an order of magnitude that speaks volumes. You may not need lightning reactions or raw power to win in golf, but you do require reserves of mental strength and stroke-making subtlety that, for whatever reasons, seem progressively to elude the ageing champions of yesteryear.

Golf may be sport’s ultimate test of nerve. You have time between shots with which to hang yourself; minutes ticking away during which the mind can get up to all sorts of mischief.

Every year we see top players committing hara-kiri, hitting the ball out of bounds or going knee-deep into water, their minds mesmerised by the proximity of the prize. Volitional control of your own destiny as you stand above the ball: that is the most thrilling and the most terrifying thing about competitive golf. But Watson did not choke, even as we expected him to.

That, of course, was the unspoken assumption hanging over Turnberry all afternoon: that the old boy would melt away in the white heat of the closing holes. That is what always happens when an ageing champion is in the mix going into the final day. But Watson was like granite. If his iron to the 72nd green had not shot forward off the turf, he would have triumphed. It was a glorious stroke, straight and true, honing in on the hole until it jumped forward, through the green and into the fringe of rough at the back. He three putted from there. And a million hearts were broken.

It is easy for us sports hacks to exaggerate the importance of what happens on football pitches, in boxing rings, on cricket grounds and golf courses. Most of it is unremittingly trivial. But there are occasions when sport transcends the field of play; when it provides us with detonations of heroism that change the way we see the world.

Ali’s triumph in Zaire was that of a former champion winding back the clock to defeat a young and seemingly invincible opponent; the triumph of a man who had come to symbolise the racial pride of a people; the triumph of a pugilist who was forced to absorb intolerable quantities of punishment about the ribs and kidneys before unleashing the iconic punch that he had saved for a career.

Watson’s doomed tilt at history was so very nearly as intense, as moving and as momentous, albeit for very different reasons. He came within an inch and a half of redefining everything we thought we knew about sport and the possibilities of age.

“Defeat tears at my guts,” he said afterwards. Ours too, Tom, ours too.