NEW YORK -- Venus Williams continued her remarkable renaissance by returning to the US Open semifinals for the first time since 2010.
Williams reached her third major semifinal of the season -- something she last did 15 years ago -- by edging two-time Wimbledon champion Petra Kvitova 6-3, 3-6, 7-6 (2) on Tuesday night to a soundtrack of thunderous partisan support under a closed roof at Arthur Ashe Stadium.
The 37-year-old Williams, who won titles at Flushing Meadows way back in 2000 and 2001, trailed 3-1 in the third set before digging out of the hole with a little help: Kvitova's eighth double-fault handed over the break that made it 3-all. Kvitova's ninth double-fault gave Williams her initial match point in the tiebreaker.
"Sometimes you have opportunities, and sometimes you take them and you don't; but it's not like you get opportunity after opportunity after opportunity in these sorts of matches," Williams said. "You have to take the ones you have."
Kvitova, seeded 13th, was hoping to prolong her comeback from a knife attack less than nine months ago by reaching the first US Open semifinal of her career. She needed surgery on her racket-holding hand after she was cut by an intruder at her home in the Czech Republic in December. She returned to the tour at the French Open in May, losing in the second round there -- and then again at Wimbledon.
Kvitova has said she still does not have full strength in her left hand. But she often was at her powerful best against No. 9 Williams, especially in the last two sets, repeatedly delivering big, flat forehands.
Neither woman played with a ton of subtlety, mainly trading stinging groundstrokes from the baseline on exchanges that grew in intensity as the 2-hour, 34-minute encounter went along.
Williams, who revealed in 2011 she had been diagnosed with an energy-sapping autoimmune disease, is the oldest women's semifinalist at any Grand Slam tournament since Martina Navratilova at Wimbledon in 1994.
But this sort of throwback run is becoming almost routine again for Williams, who made it to the Australian Open final in January, then the Wimbledon final in July.
"Definitely felt like a special match. No easy moments, not easy to hold serve or break serve," Williams said. "This match meant a lot to me, obviously, playing at home and, of course, it being a major."
She will face unseeded Sloane Stephens on Thursday in the first all-American women's semifinal in New York since 2002.
Stephens is convinced that her run to the US Open semifinals is not proof that she is back to being as good a player as she was before foot surgery took her off the tour for nearly a year. Instead, she said, it's a result of being better than ever.
Able to summon big strokes when it mattered most, Stephens reached the final four at Flushing Meadows for the first time by edging 16th-seeded Anastasija Sevastova of Latvia 6-3, 3-6, 7-6 (4) for her deepest run at any major since 2013.
"My head is a little clearer, if that makes any sense," Stephens said. "Before, obviously, I was playing well. I had won a couple tournaments and was playing well, obviously. But being injured gave me a whole new perspective on tennis, on life and just in general."
The 83rd-ranked American has won 13 of her past 15 matches, all on hard courts, reaching the semifinals at three consecutive tournaments for the only time in her career.
She was one of four U.S. women in the quarterfinals at Flushing Meadows, the most since five made it that far 15 years ago.
In the top half of the draw's quarterfinals on Wednesday, No. 1 Karolina Pliskova of the Czech Republic meets No. 20 CoCo Vandeweghe of the U.S., and No. 15 Madison Keys of the U.S. faces 418th-ranked qualifier Kaia Kanepi of Estonia.
"It's been a great two weeks for American tennis. Seeing all the American players in the draw and all of them advancing so deep and competing so well," Williams said. "It's great to see this resurgence, and I hope it can continue."
Stephens went 11 months between tournaments because of problems with her left foot.
She had an operation in January, and while forced to stay away from her sport, she found a new appreciation for it. The time off also allowed her to enjoy other aspects of life.
"I couldn't walk. I couldn't do all the things that I wanted to do. But I did get to hang out with my family and see my little cousin's soccer games and go to weddings and baby showers and stuff. All the things that I thought before I was missing out on, [now] I really wasn't," said Stephens, whose late father, John Stephens, was the 1988 NFL Offensive Rookie of the Year for the New England Patriots, and whose mother, Sybil Smith, was Boston University's first All-American in women's swimming.
"It was just kind of, like, eye-opening," Stephens added. "When I wasn't playing, like, of course I loved my time off; but when I got back to playing tennis, it was, like, this is where I want to be. This is what I love doing."
Stephens returned to competition at Wimbledon in July. She lost her first match back, and then her second, as well, at a tournament in Washington.
"I just stayed positive," said the 24-year-old Stephens, who lost in the Australian Open semifinals four years ago. "And then, yeah, look, there, semifinal, semifinal, semifinal. I couldn't really ask for a better way to come back."
Her ranking was No. 934 before this recent streak of success.
Sevastova, who beat Maria Sharapova in the fourth round, used all manner of mixed speeds and angles against Stephens, often winning points with the help of drop shots. Sevastova, trying to reach her first major semifinal, received treatment from a trainer late in the first set for a problem with her upper right leg, but she said that was not an issue the rest of the way.
Sevastova thought she had a harder time dealing with the jitters presented by the occasion than Stephens did, even acknowledging that she relied less on drop shots late because those require gumption she couldn't quite muster.
"I'm not a robot," Sevastova said. "Sorry."
Stephens was down a break at 3-1 in the third set before evening things at 3-all.
"She had better nerves in the end," Sevastova said. "She played amazing points in the end. She deserves it."