Sloane Stephens, above, returns a shot from Venus Williams during her triumph in the semifinal round of the U.S. Open. (Seth Wenig/AP)

In a winding U.S. Open semifinal of breathless rallies, ascending quality and an impromptu standing ovation from a riveted crowd, a virtuoso display of defensive tennis won out Thursday night in Arthur Ashe Stadium. As it became near-impossible for Venus Williams to get a ball past Sloane Stephens, no matter how she blasted her strokes, Stephens ran “my tail off,” as she put it, all the way to her first Grand Slam final.

Then, with the 6-1, 0-6, 7-5 score in the books, Stephens said on court, “I have no words.”

Nobody else has either. Stephens, 24, began this hard-court season in Washington five weeks ago with a ranking of No. 957 and no glaring indication she could amass 14 big-time wins against top-50 players in three tournaments in Toronto, Cincinnati and here. Yet she reached the semifinals in those first two, and will grace the final here opposite No. 16-ranked Madison Keys, who routed yet another American, CoCo Vandeweghe, by 6-1, 6-2, in the second semifinal in the first all-American final four since 1981.

“I played pretty well,” Keys said in wry understatement as she, too, found a first Grand Slam final after one previous semifinal (the 2015 Australian Open, in her case), mashing 25 winners to Vandeweghe’s nine, spraying nine unforced errors to Vandeweghe’s 22.

“She stayed hot the whole time,” a teary Vandeweghe said moments later. The whole thing lasted 66 minutes.

On to the final: Madison Keys reacts after eliminating fellow American CoCo Vandeweghe. (Julio Cortez/AP)

Yet as Keys had played both the French Open and Wimbledon this year, stalling in the second round at both, only some hopeless dreamer could have foretold this three-tournament upsurge for Stephens.

When she lost in Washington to No. 2-ranked Simona Halep, 7-6 (7-3), 6-0, she brought an 0-2 match record for all of 2017 to Toronto. By arrival in New York, she had reached No. 83 and said that had somebody mentioned reaching the final, “I would have probably passed out, because that’s what I’m ready to do now,” after 127 memorable minutes with Williams. From an 11-month absence starting in August 2016 that included foot surgery, and from a slight dip from an early prominence that came at age 20 at the 2013 Australian Open, when she reached the semifinals — “I was a baby then,” she said — she had reached the coveted Saturday.

It meant that, somehow, she had a January when she spent the season-opening Australian Open in January immovably on the couch in a cast, and a September beyond belief. “When I came back from injury, I didn’t have all of my tools,” she said. “Like, I didn’t know if I was going to be able to run down every ball, didn’t know if my power and timing were still going to be there. I didn’t know if everything was still going to be right. The only thing I had to rely on was my fight and making sure every time I was on the court I gave my all.”

Having cited the value of “a clear head” two nights prior, she still said, “I don’t know how I got here.”

“I figured out a lot, but she played great defense,” Williams said in choppy, limited remarks as a shiny chance slipped by with one final twist.

That came at the end of a third set packed with a whopping 21 exchanges of 10 or more shots between two players who showed no interest in losing. It came in a four-point sequence near the end of a match with telling statistics: Williams, boldly into her third Grand Slam semifinal this year alone (with two finals), struck 28 winners to Stephens’s 17, and six aces to Stephens’s two, but made 51 unforced errors to Stephens’s 27.

Venus Williams reached the final of two Grand Slam events in 2017 but fell just short in the U.S. Open. (Andres Kudacki/AP)

It came when Williams stood two points from victory returning at 30-all while leading 5-4 in the third. What followed was a 25-shot rally that gripped the crowd and sometimes seemed to defy geometry. The net itself seemed to bow sometimes, the better to let the shots fly over barely. At the end of all the fine flurry, Stephens sent a backhand up the line past Williams and into the corner for a clean winner.

After Stephens claimed that game with a service winner down the middle, the first two points of Williams’s service game at 5-5 turned back toward lofty stuff. On the first, Stephens continued her habit of running down everything, eventually pushing a sort of a “lob thingy; I don’t know what that was” over Williams and onto the baseline. The sheer degree of difficulty of the whole point prompted the crowd to stand.

On the second, like the first a 12-shot exchange, Stephens ran up to a short ball and directed it cross-court with a tight angle for a love-30 lead. She got six of the next seven points from there, and wound up getting 10 of the final 11, the last one on Williams’s exhausted-looking service return that croaked from the get-go. Stephens then stood and applauded Williams as the seven-time Grand Slam champion exited, her unforeseen Grand Slam year at age 37 brimming with a 20-4 match record, two finals appearances yet not quite bliss. “I’m definitely here to win my matches, not for consolations,” she said. “That definitely sums it up.”

Somehow, with her dominant sister, Serena Williams, absent since January for pregnancy and childbirth, Williams concluded her banner year fading ever so slightly to someone who spent that same January way off the tour, someone who remained in a walking boot one month before Wimbledon. Then, after losses to Alison Riske at Wimbledon and Halep in Washington, Stephens began in Toronto. She beat No. 48-ranked Yulia Putintseva, 6-7 (4-7), 6-0, 6-4, beat some Grand Slam champions in Petra Kvitova, Angelique Kerber, continued.

Eleven more high-brow wins later, on her way to her grandest summit amid the everlasting mystery of sports, she had come to see herself as “a real fighter, that I have a lot of grit.”

Then, she said: “Surprising.”