Defending champion Maria Sharapova was forced to drop a set before beating Patty Schnyder in the season-ending WTA Championships.
The Russian ace was beaten by Nicole Vaidisova in the Family Circle Cup second round.
French Open champion Anastasia Myskina lost to 15-year-old Czech Nicole Vaidisova in the second round of the Family Circle Cup.
Despite spraining her left ankle on Friday, the former world No. 1 is hopeful of playing the first round tie against Belgium.
The American ace has won all 10 semi-finals she played this season and never failed to reach the title match in Zurich in the six years she has played the event.
Davenport saved two match points to beat Hantuchova and reach the quarter-finals of the Zurich Open.
Both survived tough opening matches at the Pacific Life Open Masters Series.
The 17th seed has been in no-nonsense mood so far in Melbourne, moving through the rounds with the minimum of fanfare, but faces her biggest test against the German.
Venus Williams, who had advanced to the quarter-finals, pulled out of the China Open with a left knee injury
However, French Open champion Anastasia Myskina's run of miserable form continued when she was beaten by Switzerland's Patty Schnyder.
Amelie Mauresmo beat American Lindsay Davenport for the first time in 12 matches to enter the semi-finals of the China Open.
The world No 1 beat the American for the first time in 12 matches to enter the semi-finals of the China Open.
The second seeded American whipped Russia's Lioudmila Skavronskaia in the Bank of the West Classic.
Sania jumped 35 places to 99 in the latest world rankings.
Lindsay Davenport beat Russian Anna Chakvetadze 6-3, 6-3 to reach the final of the New Haven Open
The American will regain the world number one ranking from Russian Maria Sharapova if she reaches the final.
Serena Williams won her 750th career match to stay on track for her ninth Miami Open title when she beat Zarina Diyas of Kazakhstan 7-5 6-3 in the third round in Florida on Saturday. The world number one improved her career record to 750-125, seventh on the all-time list and just three match wins behind Lindsay Davenport's 753. Martina Navratilova sits atop the all-time list with 1,442 wins. The 34-year-old Williams will meet Russian Svetlana Kuznetsova in the fourth round. The 15th seed defeated France's Caroline Garcia 4-6 6-2 7-6(6). Unlike the last time they met, when Williams required 54 minutes and Diyas won just two games, the 22-year-old Kazak gave the American some trouble in the heat and humidity of Miami.
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