Sania and Zimbabwe's Cara, seeded fifth, faced stiff resistance from the unseeded Taipei pair of Hao-Ching Chan and Yung-Jan Chan before prevailing 6-3 6-7(8) 10-8 in the first round of the USD 5,427,105 WTA Premier tournament.
They next face Georgia's Oksana Kalashnikova and Russia's Alisa Kleybanova.
In the USD 5,649,405 men's tournament, being held simultaneously, fourth seeded Paes and his Czech partner Stepanek suffered an upset first round defeat against American Eric Butorac and Raven Klaasen 3-6 6-7 (7).
India's challenge is still alive in the men's doubles as Rohan Bopanna and Mahesh Bhupathi are yet to play.
Bopanna and his Pakistani partner Aisam-Ul-Haq Qureshi face Italian team of Simone Bolelli and Fabio Fognini.
Unseeed Bhupathi and South African Kevin Anderson are up against second seeded pair of Alexander Peya from Austria and Bruno Soares from Brazil.