The eighth seed Indo-Austrian pair recorded a 6-2 6-7 (5) 6-4 6-2 win over the unseeded Argentine-Spanish combination in two hours and 37 minutes.
Bhupathi and Knowle did not face breakpoint in any of the sets except second when they dropped their serve twice.
They also broke their rivals in the second set which was decided by a tie-breaker.
Bhupathi and Knowle will now lock horns against American Nicholas Monroe and Germany's Simon Stadler, who had beaten debutante Indian pair of Divij Sharan and Purav Raja.
Another Indian featuring today is Sania Mirza, who along with her American partner Lisel Huber, face Czech pair of Renata Voracova and Klara Zakopalova.