Richard Williams has often said that when his daughter Venus decides she can no longer afford to miss, she won’t. She showed it last night.

Faced with the relentless defense of Jelena Jankovic, Williams swung away until her shots finally went in and landed her in the U.S. Open semifinal for the first time since 2002, when she lost to her sister Serena in the final. The 4–6, 6–1, 7–6(4) victory set up a semifinal against Justine Henin, the no. 1 player in the world and the woman who knocked Serena out of the tournament Tuesday evening. Venus has not won this title since 2001.

Though the match featured much uneven tennis, it never lacked for drama. Jankovic starred in the role of tightrope artist and seemed, until the last moment, like she might pull off a daring feat despite Williams’s repeated attempts to knock her down. She repeatedly got away with lollypop serves and didn’t face a break point the entire third set, after not winning a single service game in the second set.

But the third set tiebreaker saw Jankovic, who had coaxed Williams into errors much of the evening and surprised her with some acrobatic retrieving, lose control of her forehand. Trailing 5–2 after a gutsy challenge of a close call, she still managed to flash her signature smile, as if she were a mere topspin lob, her best shot, and a full split — which she featured earlier in the match — away from escaping. Jankovic’s mother smiled, too. Venus didn’t, at least not until she had finished the match with a swinging forehand volley.

Jankovic got off to a fast start, breaking Venus on her first service game and surviving the first of many shaky service games of her own for a 2–0 lead. Jankovic’s composure, something she lost after a close call in last year’s semifinal against Justine Henin, held firm the entire set, and so did her two-handed backhand, perhaps the best of its kind in women’s tennis. She earned a second break with a backhand return — off a Williams first serve — down the line for a winner. She opened the second set with a pretty backhand lob for another break of serve, and seemed to have Williams, her shoulders slumping and her arms flailing, in a bind.

Venus, of course, had been here before. During the early rounds of Wimbledon, she looked incapable of defeating most top juniors, but by the end of the tournament, she struck the ball so well, and missed so rarely, it seemed unfair to the rest of the field to allow her to play at all. She began to punish Jankovic’s serve, one of the weakest on the tour, and use her length — both her height and her wingspan — to knock off winning volleys. She didn’t allow Jankovic another game the rest of the set, and lost a mere six points on the Serbian’s serve. Though she couldn’t quite find that range for much of the third set, she did when it mattered most.

Before Williams and Jankovic took the court, the forgotten women of the draw — those fine young ladies who were supposed to be fed to Maria Sharapova, until the defending champion double faulted her way out of the tournament — continued to fight for what everyone assumes is the right to finish second in Saturday evening’s final.

But either of the Russians who advanced to the semifinals yesterday afternoon might well walk off with the title. Svetlana Kuznetsova, the 2004 winner here and the no. 4 seed, and Anna Chakvetadze, a 20-year-old with elegant strokes that seem to carry the ball over the net to a perfect resting place, are playing the best tennis of their lives. Considering the difficult semifinal contest that awaits Henin and Williams, and the fact that the Open does not offer its finalists a day of rest, the favorite might play less than her best on Saturday.

Kuznetsova is a particularly compelling challenger. When she won this title three years ago, many in tennis thought she might race past her many Russian peers and become the Queen of the Ova generation. Kuznetsova, who trained in Spain as a junior, is adept on all surfaces, and her game is far more complete than most women on the tour, save Justine Henin and a few others. She strikes clean, powerful forehands and backhands, volleys well (she plays a lot of doubles), and serves well, too. She’s not as fit as Henin, but her legs are without a doubt the strongest, and among the fastest, on the tour (her parents are cycling champions).

Few people hear much about Kuznetsova, which simply proves that in women’s tennis, it’s still easier to receive a lot of attention if one looks like a runway model, rather than if one has blistering strokes (although it remains best to have both looks and game). Among other players on the tour, though, Kuznetsova is quite popular. Ask her if she has any habits unbecoming of a professional athlete — specifically, drinking or smoking cigarettes — and you’ll see her humorous side.

“Yeah, I smoke weed all the day,” she said, laughing during a brief interview in the player’s garden behind Arthur Ashe Stadium, after she defeated Agnes Szavay, 6–1, 6–4. “No, I’m just kidding. If would smoke weed, I would test positive. I think I’m really funny, I’m really crazy, I’m really open mind, I have very big heart, I love everybody.”

She’s also more confident, and happier, than she has been since the day she won here, and suddenly felt pressure to win more.

“I went low afterwards,” she said. “I lost confidence, I didn’t play well, I [got] down on myself. I definitely saw psychologist and everything, but the first person that helped me is myself.”

Kuznetsova has played all her matches early in the day, but she says she loves the lights of Arthur Ashe Stadium. No surprise there, considering she defeated countrywoman Elena Dementieva under those very lights for her only Grand Slam title. It wouldn’t be a surprise if she did it again this year.

Mr. Perrotta is a senior editor at Tennis magazine. He can be reached at tperrotta@nysun.com.