Sania and Swiss great Martina Hingis, seeded No.1, survived a mid-match slump to beat the 12th seeded German-American combine of Anna-Lena Groenefeld and Coco Vandeweghe 6-2 4-6 6-1.
The duo, who are on a record winning streak, will next face the 13th seeded German-Czech pair of Julia Goerges and Karolina Pliskova.
Later, Sania and Croat Ivan Dodig, also seeded top, sailed past the unseeded Kazakh-Pakistani duo of Yaroslava Shvedova and Aisam-Ul-Haq Qureshi 7-5 6-2.
As a result, Sania and Paes find themselves pitted against each other in the mixed doubles quarterfinals.
In the junior competition, fifth seeds Karman Thandi and Pranjala Yadlapalli entered the girls' doubles quarterfinals after defeating China's Siqi Cao and Jia Ren 6-4 4-6 (10-2).
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