The fifth seeds defeated unseeded Brazilian duo of Thomaz Bellucci and Joao Souza in straight sets, 7-5, 7-6 (3), in one hour and 45 minutes.
In the first set, Paes-Stepanek broke Bellucci-Souza on their second break point and sealed the set without losing a single game on their serve. Bellucci-Souza served four double faults at crucial junctures which cost them the match.
Paes-Stepanek next face the America-Australian pairing of Jesse Levine and Marinko Matosevic who overcame eleventh seeds Jonathan Marray and Frederik Nielsen 6-1, 7-6, 6-4.
Photos: Shraddha Kapoor, Kim Sharma at 'Haseena Parkar' screening
Mumbai to Goa train: First look at the glass-top Vistadome coach
Shuttler Ashwini Ponnappa keeps it short and sexy on social media
Photos: Narendra Modi, others at Marshal Arjan Singh's funeral
Photos: Sussanne Khan and Nimrat Kaur spotted at a spa in Juhu