Sania and her Chinese partner Jie Zheng, who are seeded 10th, defeated the unseeded Hungarian-American combination of Katalin Marosi and Megan Moulton-Levy 6-3, 7-5.
They will now be up against sixth seeds Anna-Lena Groenefeld of Germany and Kveta Peschke of the Czech Republic.
In the men's doubles competition, it turned out to be an equally good day for all the Indians in fray.
First up was Divij Sharan with his Chinese-Taipei partner Yen-Hsun Lu. The duo defeated the Israeli team of Jonathan Erlich and Andy Ram 6-4, 5-7, 7-6 (2) in a hard-fought contest.
They have a tough match on hand as next up for them is Pakistan's Aisam-ul-Haq Qureshi and the Netherlands Jean-Julien Rojer, a combination that is seeded fifth in the season's final Grand Slam.
Fourth seeds Leander Paes and his Czech partner Radek Stepanek also endured a tough match before rallying to beat the unseeded German-Austrian duo of Daniel Brands and Philipp Oswald 4-6, 6-3, 6-4.
Paes and Stepanek will square off against 14th-seeded Frech combine of Michael Llodra and Nicolas Mahut in their third-round match.
Elsewhere, Rohan Bopanna and his French partner Edouard Roger-Vasselin, who are seeded sixth, got the better of Russians Nikolay Davydenko and Mikhail Elgin 7-6(2), 7-6(0) in another evenly-contested match.
Bopanna and Edouard's next opponents are 12th seeded Colin Fleming and Jonathan Marray of Britain.
Image: Leander Paes and Radek Stepanek
Photograph: Alex Trautwig/Getty Images