Sania and Martina -- the reigning Wimbledon, US Open and Australian Open champions -- prevailed 7-6(4) 6-2 in the opening round of the clay court Major, which they need to win to complete their non-calendar Slam.
Sania and Martina lost their serve thrice in the match as they battled 12 breakpoints in the contest.
They next face the winners of the match between the pairs of Karin Knapp/Mandy Minella and Nao Hibino/Eri Hozumi.
The world number one team broke Kasatkina and Panova in the very first game of the second set but only to be broken back in the next.
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However, they broke them one more time and held their own for a 4-2 lead. Another break set them up for serving out the match which they did with ease, at love.
Bopanna and his Romanian partner Florin Mergea are seeded sixth and they face French team of Stephane Robert and Alexandre Sidorenko.
Paes and his Polish teammate Marcin Matkowski have been seeded 16th and they clash with Belarus' Aliaksandr Bury and Denis Istomin from Uzbekistan.
Another Indian in the fray is Purav Raja, who has teamed up with big-serving Croat Iva Karlovic. They are up against ninth seeds Lukas Kubot and Alexander Peya.
In the mixed doubles, Sania has paired with Ivan Dodig and Bopanna will play with Russia's Alla Kudryavtseva.