Svetlana Kuznetsova is back to playing her best tennis at the site of her biggest accomplishment.

Kuznetsova moved into the semifinals at the U.S. Open for the first time since winning the 2004 title, beating unseeded Agnes Szavay 6-1, 6-4 today.

“It’s my favorite tournament. I love New York,” the no. 4-seeded Kuznetsova, said. “It doesn’t matter how I feel, I just come to this court and always want to give my best.”

She’ll face another Russian next, because no. 6 Anna Chakvetadze swept the last six games to eliminate no. 18 Shahar Peer 6-4, 6-1 in the day’s first quarterfinal.

It will be Chakvetadze’s first Grand Slam semifinal. Kuznetsova can count on an edge in experience, having made it to the 2006 French Open final, in addition to claiming her only major championship at Flushing Meadows three years ago.

Since that breakthrough, though, Kuznetsova has had her problems at the American major. In 2005, she became the first defending women’s champion to lose in the U.S. Open’s first round. In 2006, she exited in the fourth round.

And now? Does she feel as though she can win the title?

“Definitely. Yes,” Kuznetsova said. “Of course I believe in myself.”

She ended an impressive U.S. Open debut by the 18-year-old Szavay. Kuznetsova gained some insight into Szavay’s game when they met in the final of a hard-court tournament at New Haven, Conn., on the last weekend of August. Szavay quit during that match because of a back injury, but recovered well to make her first major quarterfinal in only her third Slam, and she hadn’t lost a set until today.

The 20-year-old Chakvetadze never had been as far as a major quarterfinal until this year, when she lost at that stage at the Australian Open and French Open. But from 4-4 in the first set, Chakvetadze took control against Peer, the first woman from Israel to play in the U.S. Open quarterfinals.

“I just started to play more aggressive,” Chakvetadze said.

Simple as that.

“That’s why Anna is a top-10 player – she’s playing really good tennis the last few months,” Peer said, “and I think it’s just a matter of time (until) I will get there.”

The last women’s quarterfinal was scheduled for tonight, with two-time Open champ Venus Williams playing no. 3-seeded Jelena Jankovic. That was to be followed by no. 1 Roger Federer against no. 5 Andy Roddick in a quarterfinal that’s a rematch of last year’s Open final.

The complexion of both of those night matches changed a bit when the tournament took a sharp twist Tuesday night – and in the wee hours today.

Scrap that Venus vs. Serena matchup. Cancel that Rafa vs. Roger rematch, too.

First, Serena Williams departed, losing to top-seeded Justine Henin for the third straight time in a Grand Slam quarterfinal. Henin made it look easy at the end in a 7-6 (3), 6-1 victory.

“I got to go back and study and figure out how to beat her. That’s it. Bottom line,” Williams said.

Henin had a rooting interest in Williams-Jankovic: She’s 1-7 against Venus, 7-0 against Jankovic.

“Every match is a final for me now,” Henin said. “If I have to play Venus, it will be a good challenge for me to play both sisters in the same tournament.”

A lot of tennis fans were looking forward to seeing Federer meet Rafael Nadal in a third straight Grand Slam final. Won’t happen now: 15th-seeded David Ferrer upset the second-seeded Nadal 6-7 (3), 6-4, 7-6 (4), 6-2 in a fourth-round match that ended early Wednesday.

“Sure there is disappointment for me, but that is tennis,” Nadal said.

The lower deck at Arthur Ashe Stadium was mostly filled when Nadal’s shot sailed long at 1:50 a.m. It came close to the latest ending at the U.S. Open — back in 1993, Mats Wilander finished off Mikael Pernfors at 2:26 a.m.

Nadal winced and dropped to the court late in his match, a rare scene that happened right in front of his family’s box. Nadal came into the tournament with bad knees, and the left-hander needed ice for his racket hand late in the match.

“I prefer not to speak about my body right now,” Nadal said, adding it would sound like an excuse.

Nadal and Federer split the previous two Slams; Nadal beat him in the French Open final, Federer broke back at Wimbledon.

“Tonight,” Ferrer said, “all was perfect.”

Well, almost.

Early in the match, Ferrer was bothered by the overhead video screens at both ends, which sometimes show live shots during play. He complained to the chair umpire, who had tournament referee Brian Earley come out to discuss it.

“It’s unbelievable,” Ferrer told Earley. “It’s impossible to focus.”

Earley said the screens would stay on.

Henin sent a sullen Williams out of the tournament. As Williams waited for a courtesy car at the player exit, her mom gave a quick hug.

“It’s kind of like she had no energy. No get-up-and-go,” Williams’ mother said.