Flushing Meadows, NY -- (Sports Network) - Two-time champions Serena Williams and Venus Williams were a pair of easy third-round winners Saturday at the U.S. Open.

The fourth-seeded Serena blasted 30th-seeded Japanese veteran Ai Sugiyama 6-2, 6-1 in a mere 66 minutes at Ashe Stadium. The powerful American broke the overmatched Sugiyama four times and held her big serve throughout.

The eight-time major champion Serena titled here in 1999 and 2002 and is the last American woman to run the table in Flushing.

Serena could meet her fellow former No. 1 sister Venus in the quarterfinals next week. The superstar siblings are the only former U.S. Open champions remaining in the women's draw.

The 26-year-old Serena lost to Venus in the Wimbledon final last month.

A seventh-seeded Venus swatted 27th-seeded Alona Bondarenko 6-2, 6-1 in a brisk 56-minute affair at Ashe. The powerful American ripped nine aces and did not allow even one break-point chance for her overmatched Ukrainian counterpart, who had her serve broken on four occasions en route to defeat.

The reigning two-time Wimbledon champion Venus was the back-to-back U.S. Open champ in 2000 and 2001 and runner-up here in 1997 and '02. She's a seven-time major titlist, including a whopping five Wimbledon championships.

The 28-year-old Venus could have her hands full with ninth-seeded Pole Agnieszka Radwanska in a fourth-rounder here on Monday. The talented Radwanska rolled past 18th-seeded Slovakian Dominika Cibulkova 6-0, 6-3 in 1 hour, 18 minutes on Day 6 at the USTA Billie Jean King National Tennis Center.

Russian sixth seed Dinara Safina lost her first set, but rallied to take the next two and advance past Switzerland's Timea Bacsinszky 3-6, 7-5, 6-2. Safina was the French Open and Olympic runner-up and has reached the final in six of her last seven events.

Other seeds that advanced on Saturday included ninth-seeded Pole Agnieszka Radwanska, who had no problems in a 6-0, 6-3 win over Slovakia's Dominika Cibulkova, the 18th seed, and 16th-seeded Italian Flavia Pennetta knocked off 19th-seeded Russian Nadia Petrova 4-6, 6-4, 6-3.

The upset of the day saw Anna-Lena Groenfeld of Germany down 17th-seeded Frenchwoman Alize Cornet in straight sets 6-4, 7-5.

Another former world No. 1 advanced on Saturday, as 32nd-seeded Amelie Mauresmo ended the Cinderella run of fellow Frenchwoman Julie Coin in 6-4, 6-4 fashion. On Thursday, the 188th-ranked Coin posted one of the greatest upsets in tennis history by shocking top-ranked Ana Ivanovic in the second round.

Mauresmo is a two-time major titlist who has been plagued by injuries over the past two seasons. She was ranked No. 1 during the 2006 campaign.

Unseeded action saw France's Severine Bremond defeat Italian Tathiana Garbin 7-5, 3-6, 6-4.