For Caroline Wozniacki, watching her opponent being carried from the court in a wheelchair was not how she wanted to celebrate reaching the US Open final. Instead of reveling in her accomplishment, Wozniacki was worrying about Peng Shuai, who had succumbed to heat illness during their semifinal match Friday. At one point, Wozniacki had rushed around the net to comfort Peng before she decided to retire from the match.

The victory sent Wozniacki into Sunday's final against her good friend Serena Williams, the top seed, who advanced easily in the second semifinal, 6-1, 6-3, over Ekaterina Makarova. That match took exactly an hour, far from the test of endurance Wozniacki and Peng produced.

It was a test that did not end well for Peng, who received medical treatment on and off the court during the eighth game of the second set. She returned to play a few more points before collapsing on the court and retiring.

“It was really hard to watch for me whenever I saw her collapse on the court,” said Wozniacki. “You know, tennis is great, but the health is more important. You know, to see her struggling out there, I just wanted to make sure she was okay.”

The air temperature was recorded at 86 degrees Fahrenheit (30 degress Celsius), but it clearly felt far hotter on the Arthur Ashe Stadium court.

The match was being played under the WTA Tour’s extreme heat rules, and both players wore ice-filled towels during changeovers.

Peng, 28, had also struggled with the heat at the Australian Open this year, vomiting and suffering muscle cramps in a first-round loss. Hours after the match, Peng said she was feeling better.

She said she had started to feel the cramps coming on early in the second set. She did not want her first trip to a Grand Slam singles semi-final to end that way, though, so she tried to persevere, even after she had been helped off the court the first time and the doctor had told her she did not look well enough to compete.

“I said, ‘No, no, no, I don’t want to give up,’” Peng said. “I want to try one more time. And then I come back. I know I’m not going to stay maybe too long, but I just want to try, you know. I just wanted to challenge her one more time.”

The doctor and the trainer, who treated Peng with ice and water during a medical timeout, ultimately determined that she could continue playing. "If our medical staff felt the player would endanger herself by returning to the court, they would not have allowed her to return," said David Brewer, the tournament director. "And they have the right to do that."

Only after Peng had safely left the stadium could Wozniacki contemplate what she had accomplished. The victory meant she would return to the final for the first time since 2009, when she lost to Kim Clijsters. That helped boost Wozniacki into the number one ranking for much of the next year, but she never did win a major or return to another final.

This summer she is rising again. It seemed to start after golfer Rory McIlroy called off the couple’s engagement, an emotional blow that Wozniacki had to deal with very publicly. But she did so in a way that has earned her compliments for her poise and maturity. She also seemed to channel her emotions into improving her game and her fitness, announcing that she was training for the New York City Marathon.

A more powerful game helped her reach the semifinal, beating Maria Sharapova and Sara Errani in the last two rounds. She said she was a much different player than she was in 2009, for many reasons. "I have definitely learned a lot in those years," Wozniacki said. "I have had more matches under my belt. I have learned more about myself. Going out to the finals back then against Kim, I knew that it was going to be really tough. I didn't know what to expect, what to expect from my nerves. So this time it's going to be different."

Wozniacki is 1-8 against Williams in head-to-head matchups, losing in three sets twice just before the US Open, in the semi-finals in Cincinnati and the quarter-finals in Montreal. Williams said they had talked about how much better it would be if they could meet again in the US Open, but not until the final.

"I was just glad we weren't on the same side of the draw this tournament," Williams said. "Of course we were like, 'That would be great if we could see each other in the final,' because we both, you know, hadn't had the greatest Grand Slam year. We were just excited to be there." New York Times