The Indo-Czech pair defeated the Slovakian-Austrian pair 6-4 6-4 in one hour and 17 minutes in the USD 1,280,565 hard court event.
The two sides fought tooth and nail, producing a thrilling game of tennis.
Paes and Stepanek will next take on British brother pair of Andy and Jamie Murray, who rallied to beat Eric Butorac and Jarko Nieminen 5-7 6-3 10-4 in their opening round.
