Sania and Huber, lost 6-3, 3-6, 5-7 to Kveta Peschke and Francesca Schiavone on Monday.
But Leander Paes and Nenad Zimonjic failed to make it to the second round in the Nasdaq Open tennis tournament.
It was also a bad day for India's juniors at US Open on Sunday.
Bhupathi has also moved into the second round of the men's doubles events.