When Rafael Nadal said early in this tournament he was not looking forward to his next birthday, it was tempting to assume the finishing line in his career might be nearer than he cared to contemplate. In the final of the 2017 US Open on Sunday, the Peter Pan of tennis laughed at time in more ways than one, playing with the bouncing zest of his youth to breeze past Kevin Anderson in two hours and 27 minutes for his third title here and the 16th slam of his long career.

Afterwards Nadal said: “It has been a very special two weeks for me, but congratulations to Kevin. He’s a great example to a lot of kids, had a lot of tough injuries. Personally, it’s unbelievable what’s happened to me after a couple of years of injuries, playing not so good. But I’ve been playing a high level of tennis and the crowd here brings me to a higher level of energy.”

He also thanked his uncle Toni, who was watching his last slam with him as coach. “Without him I would never be playing tennis. It is great I had someone like him pushing me all the time. He had great motivation to practise with me since I was a kid. He is for sure one of the most important people in my life.”

Anderson said: “Getting to my first grand slam final, there’s been a lot of emotions for me. I’ll keep working hard. I’ll be back.”

Nadal’s 6-3, 6-3, 6-4 win was his fourth in a New York final and his fifth win over Anderson, the sort of shut-out mastery Roger Federer has imposed on other players over the years, and which the Swiss confirmed here before losing to Juan Martín del Potro in the quarters. That defeat cost New York fans a Nadal-Federer semi-final. At least bits of the old empire remained in place, despite recent upheavals.

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The big four of Nadal, Federer, Andy Murray and Novak Djokovic had won 45 of the previous 50 slams between them, with only Stan Wawrinka, Del Potro and Marin Cilic intruding on their dominance. But Anderson could not be denied his chance. He out-hit Sam Querrey in the semis and was determined to make the most of his big day – except the world No1, 18 days younger than him, was not about to co-operate.

Anderson’s big serve pinned Nadal deep, close to 10 metres behind the baseline at times, but he was palpably comfortable there. And, almost from the first exchange, the deadening pattern of struggle on one side of the net and urgency on the other began to emerge.

When Anderson tried to serve and volley for just the 20th time in the tournament, Nadal passed him for break point, and it took a third ace, swinging wide, to help him stave off three break points in the third game, which lasted 12 minutes. Nadal held to love in a twinkling.

A third double fault got Anderson into more trouble in the fifth game, but again the amiable trier his friends call “The Dog” clung on like a terrier. In the first half hour, he had not had a look at Nadal’s serve and had to save four break points. It was desperate stuff. Twice in the seventh game, the spare ball popped out of Anderson’s pocket and he acknowledged the chair umpire’s warning that a third transgression would cost him the point. It was the sort of distraction that can disrupt a player’s focus, and a fourth double fault handed Nadal a fifth break opportunity. This time Anderson cracked, pushing a forehand wide.

Within 10 minutes, the first set was Nadal’s. Anderson’s challenge in the biggest match of his life was to stop a steady drip turning into a full-scale leak. They had known each other since they were 12 – not unlike Murray and Djokovic, although the rivalry was way less competitive. Murray has won two of his three slams against the Serb; Anderson has won just one set of 12 in five matches against Nadal.

While Nadal was now rushing through the points, Anderson tried to slow the narrative, like a condemned man asking for a final piece of pie. Behind in the serving cycle, the pressure mounted. When Nadal broke to go 4-2 up in the second, there was a chilling inevitability about the rest of the match. The crowd had fallen into near slumber. Nadal was winning not only the points he fashioned himself, but those he was not expected to get, scampering after every half-chance and putting most of them away imperiously.

Anderson kept fighting but Nadal is a ruthless front-runner. He had only lost twice in his career from two sets up – to Fabio Fognini here and in Miami against Federer in the distant past – and history did not lie to him on Sunday.

Anderson’s big serve kept him vaguely competitive, but there was little he could do about the whipped forehand that gave Nadal the ninth game to love – his fourth to that point – and the set.

Anderson’s resistance slowly morphed from heartfelt to token. The first set had taken nearly an hour, the second 39 minutes, the third – despite Anderson’s first love hold to trail 3-2, a 10th ace to hold in the ninth game to make Nadal serve it out in the 10th game, and a brave battle to his first deuce point on Nadal’s serve at the very end – lasted 50 minutes. Nadal won it with his 16th volley.

While the other lions are sleeping – Murray probably for the rest of the year, Federer working on his troubled back, Djokovic and Wawrinka already out until the start of next season – Nadal, fit and strong again with his game in superb shape, will make a push that could further disturb the upper order of the game.

The next leg of the journey is the 2018 Australian Open, where he lost to Federer in the final this year.

If the Swiss does not repeat his extraordinary heroics there and Nadal prevails, he will be sitting on 17 majors, just two behind Federer. If he wins his 11th French Open in May, as he will be favoured to do, the gap will be a single title. They will then arrive at Wimbledon with even more to play for. Peter Pan, incidentally, will be 32 by then.