Paes and his Czech partner, seeded fourth, had to battle for two hours and 12 minutes to overcome 14th seeded veteran French pair of Michael Llodra and Nicolas Mahut 7-5 4-6 6-3. (Agencies)
Up next for Paes and Stepanek could be India's Divij Sharan and his 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.
Divij and Lu have a tough match on hand as they face 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.
Sania and China's Zheng, seeded 10th, took out sixth seeds Anna-Lena Groenefeld of Germany and Kveta Peschke of Czech Republic 6-2 6-3 in one hour and 12 minutes.
Sania and Zheng never faced a break points in the match and broke their rivals twice in each set to move to the last- eight pairs stage.
In the Paes-Stepanek match, after trading breaks, the opening set was on serve till the 11th game. The Indo-Czech pair had its first set point in the next game but Stepanek hit a forehand to net.
However, the Czech hit a volley winner to earn third set point, which they converted to shoot ahead.
Paes and his Czech partner, seeded fourth, had to battle for two hours and 12 minutes to overcome 14th seeded veteran French pair of Michael Llodra and Nicolas Mahut 7-5 4-6 6-3.