Sloane Stephens beat Anastasija Sevastova, 6-3, 3-6, 7-6 (7-4), to advance to the semifinals at the U.S. Open. (Don Emmert/AFP/Getty Images)

An odd duck turned up in droves Tuesday at the U.S. Open. It had been thought largely extinct. Yet it teemed around Arthur Ashe Stadium by day session and by night session, booming, buzzing and marveling.

It was the giddy American tennis fan, which used to proliferate in the 20th century but largely had vanished through this decade save for admiring the otherworldly work of one Serena Williams. But now, in the eternal slot machine of tennis ticket-buying, a risk that can subject fans to dud matches and mid-match retirements, it had pulled the arm and watched the coins gush out.

It saw two women's quarterfinals that haltingly, but steadily, spun themselves into gems. It saw Americans win them by scores so close to identical as to be uncanny. It saw two versions of that bloodcurdling thing that, among Grand Slams, happens only at the U.S. Open: the closing-set tiebreaker. Loudly, it saw 24-year-old Sloane Stephens, by day, and 37-year-old Venus Williams, by night, claim the first two available semifinal berths and forge the first two-woman American final four since 2004.

"Thank you guys so much," Stephens told the day-session crowd.

"I felt every single one of you guys behind me," Williams told the night-session crowd.

Shortly after 5 p.m., the stunning, sparkling summer of Stephens persisted when she withstood Anastasija Sevastova, the excellent No. 17-ranked Latvian, 6-3, 3-6, 7-6 (7-4). Shortly before 10 p.m., the stunning, sparkling Grand Slam year of Williams persisted when she withstood Petra Kvitova, the two-time Wimbledon champion on a compelling rebound from the horror of a knife attack last December, 6-3, 3-6, 7-6 (7-2). Both Stephens and Williams faced 3-1 deficits in third sets. Both Stephens and Williams packed big-game, airtight tennis into their tiebreakers.

Further, it actually could get headier than all that, with both Coco Vandeweghe and Madison Keys due for quarterfinals Wednesday, leaving still possible a reality that would seem bizarre in this Europe-dominated century: a first four-American set of women's semifinals since 1981.

By the end of it, near 10 p.m., Williams sat in her chair with a smile so wide and true that it really did seem to outpace almost all her smiles of all the years. In 2 hours 34 minutes, as the quality elevated she clearly had adored the pressure and the battle. To push her Grand Slam match record this year to 20-3 and reach her third set of semifinals (with two finals already), she had summoned so much of what she has learned across her 20 professional years.

"Tiebreakers, you have to play smart but you have to be aggressive," she said. "You can't just sit back and hope. I didn't want to hope. I wanted to, like, be doing something about my future."

By the end of her 2 hours 28 minutes, Stephens had reached the highest perch of a steep summertime climb from 11 idle months spent with what she called "a peg leg" and with foot surgery. A player whose layoff ended with a brief stay at Wimbledon, who had never ventured to a U.S. Open quarterfinal such as this and had never played on Arthur Ashe, looked downright seasoned. "She had better nerves," Sevastova said.

When finally Stephens drilled an I-mean-it backhand up the line for a clean winner, she had become the first American U.S. Open women's semifinalist outside the peerless Williams family since Jennifer Capriati and Lindsay Davenport in 2004.

"When I started the comeback at Wimbledon, I'd never, ever dream of something like this happening," she told the crowd. From seemingly out of the blue, she heads now for a colossal semifinal toting a bulging bag of summertime wins, 13 of them in three tournaments in Toronto and Cincinnati and here, all against top 50 players, six against top 20 players. It has had an astronomical effect on her ranking, No. 934 when she left Washington merely one month ago after one match against No. 2 Simona Halep, but No. 151 by Cincinnati, No. 83 by the start here and a projected No. 34 based on the semifinal berth.

"Honestly, we're just really grateful that she has her health back, and that's really it," said her mother, Sybil Smith, who in 1988 became the first African American all-American in swimming while at Boston University.

"Happy that my foot is good and I don't have any pain and my body's holding up," Stephens said.

Asked about Stephens's sentiment about the shock of it all, Smith said, "I share it. I share it."

Asked what changed since before the layoff, Stephens said, "I think, just, my head is a little clearer, if that makes any sense."

In winning her third three-set match out of five here, the same number as Williams, Stephens overcame one of the two top 20 Latvians, from a nation with a population (2 million) smaller than that of Brooklyn. But as Williams later would break for 3-3 in the fifth set and vow to hold her serve from there (she did), Stephens cranked a forehand on a scary break point at 1-3 that caused Sevastova to net one. Two deuces later, it was a taut gem leading to a tiebreaker, which featured the banging tension of 12-, 10-, 13- and 14-shot rallies. Stephens led 3-1. It went to 3-3. Stephens led 5-3. But at 5-4, she claimed the last two points on a netted baseline forehand from Sevastova and on that ripped backhand.

"I mean, it's a third set," Sevastova said pleasantly. "You're playing for the semifinals of the U.S. Open. I'm not a robot." Then she raved about Stephens's various talents to such degree that it sounded as if she spoke of some recent second-week Grand Slam mainstay. "As a team, her team," Smith said, "we said we're just going to take it one tournament at a time, fight hard, and add the improvements to her game, work on the improvements to her game and have a great time. That's what she's done."

More on the U.S. Open:

Men's scores | Women's scores