NEW YORK — When that emblem of career longevity Serena Williams was asked Tuesday night following her win in the U.S. Open quarterfinals why the desire to win another Grand Slam title burns hotter in her than it did before she took time off to have her daughter, she gave an answer that made tennis fans a bit weepy.

“I don’t think I have another 10 years of having opportunities to be able to play and win championships,” Williams said. “Every match really means a lot to me.”

If ever there was a reminder that fans should appreciate the game’s largest figures while they can, Tuesday night at the U.S. Open was it.

No. 1 Rafael Nadal defeated Dominic Thiem, 0-6, 6-4, 7-5, 6-7 (4-7) 7-6 (7-5), in a 4:49 marathon that ended at 2:03 a.m. Wednesday. The victory, which puts the defending champion through to his third consecutive Grand Slam semifinal, came hours after Williams booked her 12th U.S. Open semifinal and the night after Roger Federer was ousted by the unseeded Australian John Millman in the fourth round.

Nadal appreciated his victory as much as Williams appreciated hers.

“Of course, tennis is not forever. Of course, you know that your chances to play these kind of matches every time are less,” Nadal said. “But in some way, being honest, I had a very tough injury in 2005. I had the chance to really appreciate all the things that happened to me during my career because I had in different moments tough injuries. So when you are back, you always appreciate the things that happen. They have more value, more personal value, when you come back from tough moments, no?

“Yeah, of course, I played a lot of long and tough matches in my career. That’s one more today. I like this feeling, but at the same time you feel tired after that,” Nadal said.

Nadal never looked as physically spent as Federer did in Arthur Ashe Stadium on Monday night, but in a rematch of this year’s French Open final, Thiem had him on the ropes.

The Austrian, who turned 25 Monday, owns nine ATP Tour titles on clay and is considered to be a potential successor to Nadal as the best clay-court specialist in the world — in their 11 career battles (Nadal owns an 8-3 record in the series), Tuesday’s was the first on hard court. He viewed the match as an important experience in his young career.

“I would say the first really epic match I played. I played some good ones before, but not that long, not that long against the great guys on the Grand Slam stage,” Thiem said. “I’m happy that I did this for the first time, even if it went the wrong way. Of course, now I’m devastated a little bit. But in few days I will look back and will remember how great it was to play in front of a packed Arthur Ashe — this great match.”

Thiem took the first set in just 24 minutes, stunning a packed crowd at Billie Jean King National Tennis Center. It was just the fourth time in 282 career Grand Slam matches that Nadal lost a set 6-0, and the first time he won a match after that poor of a start.

What was most impressive in a match that featured brilliant shot-making and powerful, line-clipping groundstrokes over the course of nearly five hours was that Thiem looked to be the fresher player compared to the 17-time Grand Slam champion who is known for his fight on the court. He saved 12 break points, including three while serving at 5-5, 0-40 in the fifth set. When the ninth-seeded Thiem forced deuce in that game, Nadal rewarded his friend with a small clap from the other end of the court.

The Austrian was often in the driver’s seat and closed out points against Nadal, the best defender in the game, with his backhand. He had 24 backhand winners in the match out of 74 winners overall compared to Nadal’s 55, but the Spaniard was able to close when it counted. He faces Juan Martin del Potro in the semifinals Friday.

“It’s going to be stuck in my mind forever … I’m going to remember this match, for sure,” Thiem said. “I mean, it’s cruel sometimes tennis, you know, because I think this match didn’t really deserve a loser. But there had to be one.”

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