Top seeds and hot favourites, Sania and Martina scored a thumping 6-1 6-4 win over 14th seed Italian pair of Karin Knapp and Roberta Vinci in the women's doubles third round of the Clay Court Grand Slam tournament.
Serving for the match at 5-2, Sania and Martina dropped serve but returned to close the match in their favour.
In the men's doubles, India's challenge ended with the defeats of Paes and Bopanna.
10th seeds Paes and Canada's Daniel Nestor suffered a tame 2-6 4-6 defeat against sixth seed Italians Simone Bolelli and Fabio Fognini.
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Bopanna and Paes' defeat meant that their campaigns are over at Roland Garros this year, having bowed out of the mixed doubles event earlier.
Paes and Hingis had lost in the second round while Bopanna and his partner Yaroslava Shevadova were ousted in the first round.
Sania had also suffered a shock first round defeat in the opening round of the mixed doubles event with top seeded Brazilian partner Bruno Soares.