All-American semi: Venus vs. Sloane

NEW YORK — When her work was done and her first trip to the U.S. Open semifinals since 2010 secured, if just barely, Venus Williams sat in her sideline chair and beamed .

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 (7-2) Tuesday night to a soundtrack of thunderous partisan support under a closed roof at Arthur Ashe Stadium.

"I have to say, I felt every single one of you guys behind me — all 23,000," Williams told the crowd. "I mean, that feels good. It feels amazing. And I didn't want to let you guys down."

She sure didn't. Williams, 37, 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. And Kvitova's ninth double fault got Williams to match point in the tiebreaker.

Williams faces unseeded Sloane Stephens on Thursday in the first all-American women's semifinal at the Open since 2002. Stephens advanced earlier with a 6-3, 3-6, 7-6 (7-4) win over 16th-seeded Anastasija Sevastova. It's Stephens' deepest run at any major since 2013 and the apex of a recovery from foot surgery in January.

No. 13 Kvitova was hoping to prolong her comeback from a knife attack less than nine months ago by reaching her first Open semifinal. 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 at the French Open in May, losing in the second round there and at Wimbledon.

Kvitova has said she still does not have full strength in her left hand. But she was often at her powerful best against No. 9 Williams, especially in the last two sets, repeatedly delivering big, flat forehands in the 2-hour, 34-minute encounter.

"First of all, everything that she's gone through — to go through that is unbelievable, and you don't imagine that you're going to wake up one day and that's going to happen," Williams said. "So it's so wonderful to see her back and playing amazing."

Williams, who revealed in 2011 she had ban energy-sapping autoimmune disease, is the oldest women's semifinalist at a major since Martina Navratilova at Wimbledon in 1994.

But this sort of throwback run is becoming almost routine for Williams, who made it to the Australian Open final in January of this year, then the Wimbledon final in July. In 2002, she participated in three Grand Slam finals, losing each to younger sister Serena.

The older Williams made sure little sister got a mention Tuesday: When she was asked about the success of American women at this Open — 15th-seeded Madison Keys and 20th-seeded CoCo Vande­weghe play their quarterfinals today — Venus replied, "Have to give some credit to Serena."

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Stephens, ranked 83rd, has won 13 of her past 15 matches, all on hardcourt, reaching the semifinals at three consecutive tournaments for the only time in her career. She had an operation in January, and while forced out of tennis, she found a new appreciation for it.

"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, was the 1988 NFL offensive rookie of the year for the Patriots.

"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."

In the men's quarterfinals, 12th-seeded Pablo Carreno Busta of Spain had no trouble beating No. 29 Diego Schwartzman of Argentina 6-4, 6-4, 6-2.