The Indians fought their way back in the second set but lost the opening round match 1-6 6-3 1-6 in an hour and 31 minutes.
Sania and Rushmi, who was making her Olympic debut, were never serious contenders in this event and India's medal hopes rest in men's doubles and mixed doubles competitions.
Sania and Rushmi, bronze medal winners at the 2010 Commonwealth Games at home, were playing together for the first time after the Delhi Games.
The Indian pair got five chances of breaking opposition in the first set alone but they failed to convert a single one of those.
Although they came back to win the second set 6-3, the Chinese Taipei outclassed them in the decider as they raced to a 5-0 lead before the Indians pulled one game back. But it was too late in the end.
Sania will now play in the mixed doubles along with Leander Paes.
Mahesh Bhupathi and Rohan Bopanna will compete in men's doubles while Paes will begin his campaign with Vishnu Vardhan on Sunday.
Somdev will also play his first round on Sunday.