They set up a second round clash with Shikha Uberoi and Jelena Jankovic at the Bank of the West Classic in Stanford.
Clijsters and Xavier Malisse gave Belgium a 2-0 winning lead over Slovakia in the Hopman Cup.
However, French Open champion Anastasia Myskina's run of miserable form continued when she was beaten by Switzerland's Patty Schnyder.
Maria Sharapova will take on Slovakia's Daniela Hantuchova, while Amelie Mauresmo will meet Australian Alicia Molik in the semi-finals.
Sania Mirza staged a strong comeback to beat ninth seed Shahar Peer of Israel and enter the fourth round of the Pacific Life Open in Indian Wells on Sunday. The Indian ace won 6-7, 7-5, 6-3 and will next face defending champion Daniela Hantuchova of Slovakia in the Tier-I event.
The Indo-Swiss pair beat Yeu-Tzuoo Wang and Na Li 6-2, 6-2 in the first round at Australian Open
Hungarian teenager Agnes Szavay beat injured Daniela Hantuchova 7-6, 6-1 on Friday to advance to the semi-finals of the Paris Open.
Davenport saved two match points to beat Hantuchova and reach the quarter-finals of the Zurich Open.
They beat Katarina Srebotnik of Slovakia and Nenad Zimonjic of Serbia 6-4, 6-2 in the final at the US Open.
The American will regain the world number one ranking from Russian Maria Sharapova if she reaches the final.
The Indian ace was beaten in straight sets by Japan's Akiko Morigami.
She beat Kristina Brandi 7-6, 7-5 in the second round of the Western and Southern Financial Group Women's Open.
The sixth seeded Indo-US pair lost to Daniela Hantuchova of Slovakia and Fabrice Santoro at the French Open.
Maria Sharapova beat Daniela Hantuchova 6-2, 6-4 in the semi final to set up a title clash with Australian Alicia Molik.
Daniela Hantuchova was knocked out of the Swisscom Challenge after a 7-6 7-5 defeat to Paola Suarez.
Slovakia clinched a place in the Hopman Cup final for the second successive year after they beat the Netherlands 3-0.
Ashley Harkleroad accounted for the scalp of Hantuchova while Kafelnikov lost to Flavio Saretta at the French Open.\n\n
The duo meet in the semi-finals of the German Open.
Lindsay Davenport and Jennifer Capriati will clash for a place in the final of the Bausch and Lomb championships.
The second-seeded Russian beat Daniela Hantuchova 2-6, 7-6, 6-4 to win the Eastbourne International.
The Slovak will meet Svetlana Kuznetsova in the final of the Eastbourne International.
They beat Slovakia in the final of the $A1 million mixed team event.
Lleyton Hewitt beat Slovakia's Karol Kucera to bring Australia level in their Hopman Cup tie.
A feisty Shinobu Asagoe reduced Daniela Hantuchova to tears of frustration as she overcame the ninth seed 0-6, 6-4, 12-10.
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