Mirza and Schiavone beat wild cards Svetlana Kuznetsova and Amelie Mauresmo 6-4, 6-4 in the first round.
They next face the winner of the first round match between top seeds Cara Black-Liezel Huber and the Chinese duo of Shuai Peng and Tiantian Sun.
Sania begins her singles campaign in the Tier-II event on Tuesday when she takes on Russian qualifier Vera Dushevina.
Photograph: Karim Sahib/AFP/Getty Images