The 16-year-old Williams, playing in her first event of the year, qualified for the tournament on a wild card. Williams, ranked 211th, won two qualifying rounds and three main draw matches to reach the quarter-finals where she will play the American Lindsay Davenport. Williams and Majoli had to battle for two hours and 33 minutes under a scorching sun.
Mark Philippoussis, who recently recorded the fastest serve on the ATP Tour, served 23 aces as he defeated Andre Agassi 7-6, 7-6 in the second round of the Newsweek Champions Cup at the same venue.
Philippoussis, the winner of last week's Franklin Classic in Scottsdale, Arizona, was facing Agassi, the former world No 1, for the first time, but his serving overpowered the American who suffered his third successive first-round defeat.
Rover announced yesterday that they would be expanding their junior tennis initiative by pledging a further pounds 2m over the next two years.