FLUSHING, New York (Ticker) -- Serena Williams avenged her loss of a year ago to fellow American Lindsay Davenport, beating the third seed in a thrilling three-set quarterfinal Tuesday night at the U.S. Open.

The 10th-seeded Williams defeated Davenport, 6-3, 6-7 (7-9), 7-5 to advance to the semifinals against top seed Martina Hingis of Switzerland.

Hingis and fellow top seed Gustavo Kuerten of Brazil, still seeking to justify their world No. 1 rankings, both advanced Tuesday with straight-sets victories.

Hingis routed her childhood friend, unseeded 18-year-old Daja Bedanova of the Czech Republic, 6-2, 6-0, in just 42 minutes to reach the semifinals. Kuerten defeated unseeded Albert Costa of Spain, 6-4, 6-4, 7-6 (9-7) in a fourth-round match.

In a highly anticipated matchup of former champions, Williams and Davenport exchanged punishing groundstrokes and powerful serves. Williams, the 1999 champion, appeared to be in control when she took the last three games of the first set and the opening two games of the second set.

But Davenport broke Williams for the first time in the sixth game to even the second set. They held serve to the tiebreaker, in which Davenport fought off two match points. Williams took a 5-4 lead on Davenport's fourth of six double faults and had a chance to serve out the match but hit a backhand wide.

Davenport's long backhand gave Williams her first match point, but Williams missed a backhand that fell inches over the back line, tying it again. Facing a second match point, Davenport hit a tremendous return of serve that set up a forehand winner down the line. She won the next two points and the tiebreaker.

Williams again looked in control after winning the first three games in the third set. She blew two break points but still was serving at 4-2, 40-love when she double-faulted and opened the door of opportunity for Davenport, who broke again.

"I had a couple chances, especially in the third," Williams said. "I had my chances in the second, too. I shouldn't have lost my serve. But in the third, I had a chance to be up 4-love. I just blew it. That's what I told myself, no matter what I do, no matter how hard I wish, I couldn't even pay a person to rewind time, so I may as well get over it. That's what I was able to do. I was able to move on after that."

Davenport squandered a break opportunity in the ninth game as Williams delivered three straight strong serves to hold. The third match point was the charm for Williams, who ran down two straight baseline shots and ended it by ripping a cross-court forehand winner.

"I was always in a hole, coming back. Even after I won the second set, I got down 3-love right away," lamented Davenport. "When I got the break back, I got broken again. I kept fighting back.

"At 4-all, I had the one chance to break, and didn't. In a match like that, there's not a whole lot separating the players. I mean, a couple of points, I would have won."

The 1998 champion, Davenport dealt Williams a straight-sets loss in last year's quarterfinal encounter but has lost seven of nine matches to Williams.

In 1999, Williams became the lowest seed in the Open era to win the event, surprising the field as a No. 7. She claimed her 10th career title by beating Jennifer Capriati at Toronto last month and made the quarterfinals at both the Australian and French Open championships.

To win her second U.S. Open crown in three years, Williams may have to beat three straight former champions, including possibly her sister, Venus, in the final. Next up is Hingis.

"I just have to keep down the errors. I can't make as many errors as I did today," said Williams, who committed 40 unforced errors against 44 winners and 11 aces. "And power, sometimes you can use your power, but sometimes you want to use more brain as opposed to brawn. You don't want to have all brawn and no brain. I'm going to go out there and try and use a little of both."

In a fourth-round men's match, seventh seed Yevgeny Kafelnikov of Russia advanced easily, ousting No. 12 Arnaud Clement of France, 6-3, 6-4, 6-3.

Two other fourth-round matches featuring the young guns of the men's tour were scheduled for Tuesday.

The day match between fourth seed Lleyton Hewitt of Australia and No. 16 Tommy Haas of Germany was postponed by rain with Haas leading, 6-3, 2-2. It will be completed Wednesday morning.

Andy Roddick of the United States overpowered Tommy Robredo of Spain, 6-2, 6-2, 6-4, in a night duel between 19-year-old budding stars and the two youngest players remaining in the men's draw.

"I'm feeling really good," said the hard-serving Roddick, who has played three of his four matches at night. "The crowd's been great. They've been behind me. They make matches here unlike any place in the world."

Hingis has maintained her No. 1 ranking despite not winning a Grand Slam event in nearly two years, covering 10 tournaments. She now has made the semifinals or better in six consecutive Opens and owns five Grand Slam titles.

Hingis and Bedanova often practiced together as children in the former Czechoslovakia. They had never played as professionals and Hingis had to be a bit wary after Bedanova upset seventh seed and two-time champion Monica Seles to reach the quarters.

"You can't rush. You shouldn't hurry with her," Hingis said. "I know her game pretty well. Just don't go crazy, that's all."

But Hingis won the first 11 points of the match and never was headed. Bedanova broke back to forge a 2-2 tie but she did not win another game as Hingis continued to apply pressure in the second set.

Obviously nervous in her first appearance at Arthur Ashe Stadium, Bedanova had only six winners and 22 unforced errors.

"I was a little nervous when I came out on the court," she said. "As I stepped on the court today, I didn't feel as well as I did the past few days. Martina played really good, solid tennis. It just wasn't my best day."

Kuerten hit 18 aces and allowed only one break opportunity to Costa, who was coming off an upset of 15th seed and Wimbledon champion Goran Ivanisevic of Croatia in straight sets.

Kuerten, the three-time French Open champion, is the world's No. 1 player but his ranking is largely due to his prowess on clay. He never has been past the quarters of a Grand Slam on hard court or grass. He even skipped Wimbledon this year after winning his third French Open title.

The win was Kuerten's sixth straight over Costa, including two on a hard court. Kuerten improved to 20-6 on hard courts this year.

Kuerten will play Kafelnikov in the quarterfinals. He holds a 7-3 edge in the all-time series.

In his first two matches, Kafelnikov was taken to five sets by Swiss players Michel Kratochvil and George Bastl, then needed four sets to defeat qualifier David Nalbandian.

With Tuesday's victory, Kafelnikov clinched only his second quarterfinal berth in seven U.S. Open appearances. His best showing came in 1999, when he made the semifinals.

Kafelnikov had lost his three straight matches with Clement after winning the first two. The Russian had to wait out an 80-minute rain delay, leading 3-0 in the third set.

"I was just so into the match that I wanted to finish the match as soon as possible," Kafelnikov said. "You never know what's going to happen when you walk off the court with a rain delay. Luckily, I played two solid service games at love. It just gave me good confidence to finish the match.

"Arnaud is a tough competitor. I didn't want to give him a rhythm. I stuck to my game plan and it worked out well."

Clement upset American star Andre Agassi in the second round last year and made it to the quarterfinals before being stopped by Hewitt.

Roddick upset No. 11 Alex Corretja of Spain in straight sets to earn his first fourth-round berth in Grand Slam play. The 2000 U.S. Open junior champion has won three titles in his first full year on tour and is on a 10-match winning streak after taking the title in Washington just before the Open.

Robredo knocked off fifth-seeded fellow Spaniard Juan Carlos Ferrero to reach the fourth round in only his fifth hardcourt tournament. He also made the fourth round of the French Open.