NYTimes

In the end, amid his traditional tears at Melbourne Park, the most remarkable part of Roger Federer’s 20th Grand Slam singles title was that it came as no surprise.

Not even at age 36 in a sport where the spoils have generally been reserved for a much younger crowd.

Federer, like Serena Williams, has redefined the limits. After going nearly five years without a major, he has now won three of the last five Grand Slam tournaments.

On Sunday, under a closed roof in Rod Laver Arena, he secured his sixth Australian Open by holding on to defeat Marin Cilic, 6-2, 6-7 (5-7), 6-3, 3-6, 6-1.

Federer is the oldest man to win the Australian Open since one of his role models, Ken Rosewall, in 1972. Back then, this event was played on grass in the much more intimate setting of the Kooyong Lawn Tennis Club, with no retractable roofs in sight.

Federer is no underdog at this late stage of his tennis career. Though seeded No. 2 behind Rafael Nadal, he was the clear favorite coming into the event, even if he resisted that label.

“I don’t think a 36-year-old should be a favorite of a tournament,” Federer said before the tournament began. “It should not be the case.”

But he proved the pundits correct, defending the title he won much more unexpectedly last year, when he was returning from a six-month break to heal a lingering knee problem.

That surprise victory, secured after a series of marathon matches, meant so much to him. But Sunday night’s five-set victory over the sixth-seeded Cilic clearly resonated deeply with him, too. Federer broke down in tears — not for the first time — during the trophy ceremony in Rod Laver Arena as Laver himself was taking pictures with his phone from the front row.

“The fairy tale continues, for us, for me,” Federer said, looking toward his team and his family in the players box and fighting to keep his composure. “After the great year I had last year, it’s incredible.”

This has been one of the most remarkable late-career runs in any sports’ history. And though Federer did not lose a set on his way to Sunday’s final, Cilic pushed him to a fifth with his power game as Federer’s first serve deserted him in patches.

What had started as a rout, with Federer winning the first set in just 24 minutes, turned into a much more complicated matter.

But Federer fought off two break points on his serve in the first game of the fifth set and then broke Cilic in the next game. He challenged a second serve at 30-30 that turned out to be a double fault, then hit a deep return on the next point that Cilic failed to handle.

Federer held serve to up by 3-0 in the next tense game and then accelerated to the finish line, one he has crossed more than any men’s tennis player at the major championships that define careers, even more so in this era than in Rosewall’s and Laver’s.

Neither Rosewall nor Laver got to play a Grand Slam final under a closed roof, and though it was not raining on Sunday, the heat in Melbourne spiked again, hitting 103 degrees Fahrenheit (39 degrees Celsius) in the late afternoon. Even though the final was to begin at 7:30 p.m., the organizers determined that the combination of high temperature and humidity called for them to put in effect their extreme-heat policy and play the final indoors.

Some former players, including the Australian star Pat Cash, cried foul, but Tennis Australia officials defended the decision. After the match, Cilic said that he was surprised by the decision to close the roof, and that the change in conditions had affected him, particularly in the first set.

The grueling, three-set women’s final on Saturday night, in which Caroline Wozniacki defeated Simona Halep, was played on a slightly cooler evening with the roof open. ESPN reported that after the match was over, Halep spent several hours overnight in the hospital being treated for dehydration.

Tennis Australia officials said on Sunday that Halep’s health problems had not factored into the decision to close the roof on Sunday.

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Fatigue did not seem to play a role in the three-hour men’s final, although Federer made it clear just how taut his nerves had been.

“I think that’s why I was so bloody emotional again at the end, because I was thinking about the outcome all day,” he said. “During the first set. During the second. During the third. During the fourth. ‘How would I feel if I lost? How would I feel if I won?’ And it just wouldn’t stop, and I think that’s why this match was particularly difficult today.

“It reminded me a little bit of 2006, when I really got to the finals in a great way and played that match against Marcos Baghdatis that was also nerve-racking. I was the big favorite going in, and in the end you win and you are so relieved.”

Last year’s tournament was all about delight for Federer. He had not won a major title since Wimbledon in 2012, and headed merrily home to Switzerland with a replica of the Norman Brookes Challenge Cup, the trophy awarded to the Australian Open men’s singles champion.

Federer took celebratory photos with “Norman” high in the Alps.

“I’ve had dinner with Norman, spent a lot of time with Norman,” he said straight-faced in February. “I know it’s just a replica, but that’s all right.”

At that stage, he genuinely believed that might have been his last major title. Instead, he has gone on to win Wimbledon for the eighth time, and now the Australian Open to increase his record total of men’s Grand Slam singles titles.

It has been nearly 15 years since Federer, with a ponytail and stubble, won his first major at Wimbledon. It has been 14 years since he won his first title in Melbourne — with a ponytail and no stubble.

But while the other members of his peer group have retired (see Marat Safin, Andy Roddick and Juan Carlos Ferrero) or become very occasional doubles specialists (see Lleyton Hewitt), Federer keeps adding loot to his collection and layers to his legacy.

Even his younger rivals are suffering physically. Andy Murray, 30, just had hip surgery. Novak Djokovic, 30, played here after a six-month break because of elbow problems, but he was still in pain and is now considering surgery. Stan Wawrinka, 32, returned to Melbourne from knee surgery and looked nowhere near top form as he lost in the second round to the American outsider Tennys Sandgren.

Injuries have forced Nadal, 31, to withdraw or retire from his last two official tournaments. Against Cilic in the fifth set of the quarterfinals here, Nadal retired, but he will retain his world No. 1 ranking on Monday.

Yet Federer glides on at an age when nearly all of the great men’s players have moved on.

“There’s some good young guys coming, but we need Roger for a little while longer,” said Neville Godwin, the coach of Hyeon Chung, the rising star from South Korea who retired here with blisters on both feet during a semifinal against Federer.

With his sixth triumph in Melbourne, Federer tied Djokovic and Roy Emerson for the most Australian men’s singles titles. He is now 9-1 against Cilic, whom he defeated in last year’s Wimbledon final in straight sets.

During that match, Cilic, suffering from deep foot blisters of his own, cried in frustration during a changeover at his inability to compete at full strength.

He and Federer have since spent an increasing amount of time together off the court.

Last September, they were part of the winning European team in the inaugural Laver Cup, the event created by Federer and his management company. In late November, they ended up vacationing on the same island in the Maldives, where they had drinks and dessert and even practiced together twice.

“We were both looking for a hitting partner, and it happened that we were there,” Federer said. “It was the weirdest thing.”

But on Sunday, they exchanged tennis blows in a much more public place, and as has been the case so often in the last 15 years, the man who ended up as the champion was Federer.