Sania and her Czech partner Barbora Strycova beat Australian-Chinese pair of Samantha Stosur and Shuai Zhang 6-1, 6-4.
The fourth seeds needed an hour and 21 minutes to win. The Indo-Czech pair will play against Japan’s Eri Hozumi and Miyu Kato.
But Bopanna and his Uruguayan partner Pablo Cuevas lost to unseeded Australian pair of Alex Bolt and Bradley Mousley in the second round 6-2, 6-7 (2), 4-6.
The 15th seed were beaten in one hour and 55 minutes. Bopanna’s loss ended India’s challenge in the men’s doubles competition after veteran Leander Peas, partnering Brazilian Andre Sa, and Purav Raja and Divij Sharan lost in the first round on Thursday.
Sania-Barbora broke serve twice to claim an early 4-0 lead. That lead was enough for them to win the first set comfortably 6-1.
Stosur-Zhang responded in the second set, breaking Sania’s serve in the second game and then consolidated holding their serve to go 3-0 ahead.
The Indo-Czech pair pulled level, winning the next three games straight and then capitalised on another break to go 5-4 up.
They then saved five break points and required four match points to win the second set and the contest.