Kournikova battled bravely

Kournikova's frustration showed as the game wore on and she questioned several line calls.

But a string of unforced errors cost her dearly with Williams' powerful serve also doing damage as the game wore on.

Williams will play American Lisa Raymond in the last four.

Raymond caused the biggest surprise of the quarter-finals with a straight sets win over Monica Seles.

The third seed was beaten 6-4 6-2 by Raymond, better known as a doubles specialist.

Raymond served eight aces in the match and was never broken, taking advantage of the slow-moving Seles.

Lindsay Davenport continued her comeback from injury with a comfortable 6-2 6-2 success over Jelena Dokic in just 48 minutes.

Davenport takes a break during her match

Davenport will next meet defending champion Kim Clijsters of Belgium in a repeat of last year's final.

Clijsters ended the run of 17-year-old Yugolslav Jelena Jankovic with a 7-5 6-3 win.

Davenport is playing in her first tour event for nine months because of a knee injury but made it six wins out of six against Dokic.

"I'm amazed," said Davenport. "I didn't know what to expect this weekend but everything feels normal again, it just seems to be falling into place.

"This is the time of year you normally get tired but I feel rejuvenated."

"I didn't play my best or move well, but she had a lot to do with that," admitted Dokic.

"She made it hard for me to get a rhythm. I haven't played a player who hits that hard for a while."

Results:

Quarter-finals: