The fifth-seeded Indo-Czech combo took an hour and 45 minutes to register a 7-5 7-6 (7-3) victory over their unseeded opponents.
Even as the Brazilian pair failed to convert the lone breakpoint they earned in the first set, Paes and Stepanek converted one of the two breakpoints they managed to seal the set.
However, the Indo-Czech combo, which had won the Australian Open title earlier this year, wasted as many as five of the six breakpoints in the second which went into the tiebreaker.
In the tiebreaker though, they held their nerves to walk away with the set as well as the match.
They next play Jesse Levine of USA and Australia's Marinko Matosevic, who had upset Wimbledon champions Jonathan Marray and Frederik Nielsen 6-1 6-7(6) 6-4.