Paris ? Serena Williams won her fourth-round match and won over French Open fans Sunday.

Jeered earlier in the tournament, Williams drew only cheers after beating Shinobu Asagoe 6-3, 6-1.

Williams was joined in Tuesday’s quarterfinals a short time later by older sister Venus, who beat Fabiola Zuluaga 6-1, 7-6 (3). The sisters could meet in the semifinals.

No. 7-seeded Jennifer Capriati overcame a thigh strain to beat No. 17 Francesca Schiavone 7-5, 6-1 and will play Serena Williams next.

“I’m definitely improving match after match,” Serena Williams said.

Venus Williams raced to a 5-0 lead against the No. 23-seeded Zuluaga but struggled down the stretch. Williams, who has been plagued by injuries that included an abdominal strain last year, appeared to clutch her stomach and wince at least twice but was healthy enough to hit 28 winners.

“While I would have liked to have had an easier match, I think it’s important for me to be tested early on,” said Williams, who’s seeded fourth.

Venus’ opponent in the quarterfinals will be No. 6 Anastasia Myskina, who overcame a match point to beat Russian compatriot Svetlana Kuznetsova 1-6, 6-4, 8-6.

Unable to overcome an injury was Lindsay Davenport, who lost again in the only Grand Slam event she’s never won. Erratic and hampered by a sore knee, the No. 5-seeded Davenport was beaten by Elena Dementieva 6-1, 6-3.

Serena Williams returns to Shinobu Asagoe of Japan during a fourth round match Sunday at the French Open. Williams claimed a straight set victory, advancing to the quarterfinals with sister, Venus.

Davenport said she hurt her right knee in the second round Wednesday, then aggravated the injury in the second set against Dementieva.

No. 9 Tim Henman earned his first quarterfinal berth in a major event other than Wimbledon by rallying past French wild card entrant Michael Llodra 6-7 (2), 4-6, 6-4, 6-3, 9-7.