Sania, who recently reached her career best doubles ranking of No.5 for the second time, and her Chinese Taipei partner Su-Wei Hsieh were stunned by the unseeded Canadian-Polish pair of Gabriela Dabrowski and Alicja Rosolska 6-7, 4-6.
Sania though restored some pride in the mixed doubles event, when she combined with Bruno Soares of Brazil, and the top-seeded pair dispatched Timea Babos and Eric Butorac in double quick time 6-1, 4-6 [10-3].
Earlier the second-seeded Sania and Hsieh, who had an easy first outing against the Argentine-Swiss combine of Maria Irigoyen and Romina Oprandi in the opening round, were up against a resilient Gabriela and Alicja this time around.
Fighting hard for the first set, Sania and Hsieh finally went down in tie break after an intense 58-minute battle. Their relatively inexperienced opponents then gained confidence in the second set to comfortably dispatch the much fancied pair.
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Paes though did put a good show alongwith Klaasen but the tenth-seeded duo went down to the Italian pair after letting go of a first set advantage.
Mahesh Bhupathi, alongwith Jurgen Melzer, had already crashed out in the after the Indo-Austrian pair lost to Diego Schwartzman and Horacio Zeballos 4-6, 3-6 yesterday.
In the mixed doubles draw, Bhupathi has paired up with Jarmila Gajdosova of Australia, Bopanna combines with Czech Republic partner B Zahlavova Strycova and Paes is set to partner Martina Hingis.