Cheered on by a sizeable Indian crowd, Paes and Sania won 6-2, 6-4 in a match that lasted 64 minutes.
Paes and Sania next face top seeds Belarusian pair of Victoria Azarenka and Max Mirnyi, who won 6-2, 6-2 against the German duo Angelique Kerber and Philipp Petzschner.
Paes and Sania took a 2-1 lead in the first set before the Serbians clawed back to level at 2-2. The Indians, however, were unstoppable and won four games on the trot.
In the second set, the Serbians were playing a catch-up job with the Indians. Paes and Saina led 3-1 before going on to wrap up the match at 6-4.