In perhaps the greatest and certainly least likely triumph of his career, Roger Federer defeated his nemesis Rafael Nadal in the Australian Open final, the Swiss clinching his 18th grand slam title and all but altering the space‑time continuum in a five-set classic at the Rod Laver Arena.

With this breathtaking victory – 6-4, 3-6, 6-1, 3-6, 6-3 in three hours and 37 minutes – Federer becomes the first man to take five or more titles at three grand slam events and, at 35, the second-oldest man behind Ken Rosewall to win a major singles trophy. Only the appearance of a wooden racket could have made it more surreal.

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The fifth set was full of agonising drama and Federer weathered two break points to serve it out – but his ethereal grace could not be denied. Coming as it does a full five years after his 17th crown, the sight of the great champion’s tearful celebration was as pleasingly familiar as it was utterly astonishing. In future years he will surely look back on this ninth grand slam final meeting with his most fearsome opponent and wonder if it really happened.

The early stages of the first set provided a familiar sight – both players trying to limit the damage wrought by the other’s forehand weaponry. Federer, only the No17 seed here, was as balletic and graceful as ever and it stayed on serve until the seventh game – Nadal’s fourth on serve – when Federer unfurled an unreturnable backhand and then an imperious forehand winner before achieving the first break.

With economy of effort and an outswinging ace to seal it, Federer had taken the first set 6-4 in 34 minutes. Simply hanging in points had not been enough for Nadal. He trailed 13-5 for winners as the Swiss master went to work.

By then the arena was packed with true believers but worship had not come cheap. A day earlier tickets were being hawked for up to A$16,000 (£9,630) – more than it cost to buy a house in Melbourne when the guest of honour, Rod Laver, won his last title and quite a premium on their original price range of A$413 to A$662 (£248-£398).

Nadal needed to return with energy and hope for some untimely break in Federer’s effortless momentum in the second set. The two forces intersected to produce a pair of early break opportunities and the Spaniard struck. His battle to hold serve next up elevated the contest to fever pitch and Federer’s error count was steadily building.

As in the third set of his semi-final win against Stan Wawrinka, Federer was suddenly a shadow of the player who had been commanding the contest moments earlier and quickly trailed 4-0. Unlike that previous match, he refused simply to write off the set entirely, breaking back once and giving Nadal hell in some barnstorming rallies before conceding it 6-3 in 42 minutes.

Federer mixed howlers with howitzers in an awkward, 10-minute long hold of serve to start the third set, then just as quickly returned to his virtuoso earlier self. He unfurled a series of mesmerising forehand winners to secure an early break and wedge his foot in the door. Nadal was still stoic and mean but dropped the set 6-1. Federer had hit 18 winners to Nadal’s four and looked invincible once more.

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The No9 seed, though, was far from done. With a sizzling forehand winner down the line in the fourth game of the fourth set, he had three break points and took advantage. A sliced forehand winner to make it 4-1 in his favour bent logic and a tight angle to astound the Melbourne crowd. In 40 taut minutes Nadal had pushed it to a decider.

The only surprise when Federer took a medical time-out before the fifth set was that neither battle-weary player had done so sooner. Hopping about energetically as he waited, Nadal was soon tucking into his opponent’s serve, whip-cracking a signature forehand winner on his way to an early break.

Then Federer rallied again. His effort to break back and lock it up at 3-3 came after several moments of unbearable drama as Nadal, seemingly possessed, met almost every break point with a winner. Back on level terms, now it was Nadal showing fatigue as he sent an exhausted double fault into the middle before conceding the final, fatal break.

Almost prostrate 30 minutes previously, Federer weathered a number of nerve-shredding moments in his final service game but after an unsuccessful challenge from his opponent, finally saluted. By that point you had started to wonder whether 16-grand seats were not a bargain after all.

“I don’t think either of us believed we’d be in the finals,” Federer said afterwards before paying tribute to Nadal. “I’m happy for you. I would have been happy to lose, to be honest. The comeback was as perfect as it was.”

Play Video 0:54 Roger Federer speaks after winning Australian Open – video

Nadal said: “Today was a great match. Roger deserved it a bit more than me. I’m just going to keep trying. I feel I am back at a very high level, so I’m going to carry on fighting the whole season.”

The pointy end of this tournament taught us that sometimes the fountain of youth is actually a mirage. When the favourites Novak Djokovic and Andy Murray stumbled to shock losses in week one, it really should have been a newer-generation top-10 player such as Milos Raonic, Kei Nishikori or Dominic Thiem seizing this moment – or more likely battled-hardened Stan Wawrinka. Yet none had it in him. None had this in him.

All the while Federer and Nadal were essentially playing from memory but what temples of sporting genius their minds and bodies are. Nadal has beaten Federer so many times over the years some hesitate to call it a rivalry. Here the only shame, as ever, was the need to split them. Performing at this level in your prime is one thing; doing it as the lights dim is the mark of untouchable greatness.