Roger Federer moved a step closer to unsurpassed greatness yesterday by winning his fifth consecutive U.S. Open title and 13th major title overall, one fewer than Pete Sampras.

In the first Monday final at the National Tennis Center in Flushing since 1987, Federer defeated Andy Murray 6-2, 7-5, 6-2 with a display of precision, power, and gracefulness that put an end to any doubts about his future. Federer no longer holds the no. 1 ranking, no longer calls himself Wimbledon champion, no longer seems superior to everyone he plays. But in New York, a champion he remains. He is the only man in the Open Era, which began in 1968, to win five consecutive U.S. Open titles, and the first to do it since Bill Tilden won his sixth straight in 1925. He’s also the only man in history to win five consecutive titles both at the U.S. Open and at Wimbledon.

Federer took an early lead with a flurry of winners and then fended off the determined and creative Murray in a tense second set. At one point, Federer lost seven consecutive points on serve and was within a stroke of falling behind. He escaped from a 0-40 deficit with the help of a missed line call in the middle of a rally that Murray, engrossed in the moment, failed to challenge. (Replays showed that Murray would have won the game had the correct call been made.) Federer held serve the rest of the match until late in the third set, when he led 5-1.

By then, Murray, the 21-year-old Scot whose beguiling angles, spins, and drop shots had blunted the baseline attack of Rafael Nadal in the semifinals, had no energy for a comeback, no tricks that Federer couldn’t dismiss with his trademark forehand or a foray to the net — a tactic that he employed often yesterday. On the final point, Murray gamely defended one last Federer assault as the defending champion moved forward and Murray retreated farther behind the baseline. It was, in brief, the story of the match: Federer on the move, attacking, and Murray ducking for cover. As Federer accepted his trophy, he said he didn’t plan on staying behind Sampras for very long.

“One thing’s for sure, I’m not going to stop at 13, right?” Federer said. “That would be terrible.”

For anyone other than Federer, the first eight months of 2008 would be remembered as splendid. He reached the semifinals of the Australian Open despite suffering from mononucleosis. He played in his third consecutive French Open final. He reached the Wimbledon final for the sixth straight year and lost the finest match in tennis history 9-7 in the fifth set to Nadal. He then flew to Beijing and won a gold medal in doubles with partner Stanislas Wawrinka.

Yet Federer has so redefined the role of a champion that this outstanding stretch seemed disastrous. When he returned to tennis after Wimbledon, Federer added to the worries when he lost to lesser opponents — relinquishing the no. 1 ranking that he had held for four and a half years — and failed to win a medal in singles at the Beijing Olympics, a goal he had described as one of the most important of his career. When he arrived in New York for the U.S. Open, he had yet to win a title on a hard court this season — a troubling fact for the man many consider the finest hard-court player in the history of the game.

Murray, who joked that his $1 million runner-up check was worth “about 10 pounds,” said he had a few sarcastic words for the champion when he shook Federer’s hand across the net.

“I said that I agreed with everyone that he’s had a terrible year,” Murray said, barely smiling as the roomful of reporters laughed.

Federer’s road to this title wasn’t the most difficult he has faced and his play, at times, wasn’t pretty. Midway through the tournament he needed five sets to defeat Igor Andreev, a Russian who has had little success at the U.S. Open and on hard courts in general. That victory proved the most important of the tournament. Two rounds later, a relaxed and confident Federer served 20 aces, fired forehands to far away corners, and exacted a bit of revenge. His victim? Novak Djokovic, the brash Serb who knocked Federer out of the Australian Open in straight sets and boldly announced that the changing of the guard had begun. Murray prevented Federer from taking another crack at Nadal, but one can be sure Federer can’t wait until they meet again.

It won’t be easy for the 27-year-old Federer to match, and then surpass, Sampras’s all-time record of 14 major titles. The next generation — Nadal, Djokovic, and Murray — is among the most talented the game has ever seen. All these men are versatile, all of them are quick, fit, strong, determined, and confident. Two years ago, only one tennis player in the world, Nadal, believed he could beat Federer, and even then it wasn’t likely to happen on any surface other than clay. Now, three men know they can win against the former world no. 1 and believe they can do it anywhere.

At least now, though, we know that Federer won’t shrink from the toughest challenge of his career. He didn’t play his level best this tournament, but he played with a joy we haven’t seen from him in some time. Federer isn’t about to walk away from tennis because he doesn’t have the aura of invincibility he once had. If we’ve learned anything from this U.S. Open, it’s that greatness — true greatness — isn’t diminished by a few strong blows.

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After five years, several injuries, and many doubts about whether she would ever regain her old form, Serena Williams is back on top of women’s tennis. Williams won her third U.S. Open title on Sunday evening and now has nine major titles to her name, two more than her sister Venus.

How long can she stay there? Long enough, one hopes, for a new woman to come along and take command of the tour. When Justine Henin retired earlier this year, leaving the no. 1 ranking vacant, a few members of the next generation — Ana Ivanovic and Jelena Jankovic, the U.S. Open finalist — briefly stepped into the top spot. At this point, neither of them is ready to remain there. Neither has the presence of either Venus or Serena. Maria Sharapova comes close, though her shoulder injury is worrisome. All this is to say, the return of the Williams sisters couldn’t be better timed for the game. The sport needs them to stick around for years to come.

Mr. Perrotta is a senior editor at Tennis magazine. He can be reached at tperrotta@tennismagazine.com.