Fourth seeded Indo-Romanian team was fluent in their 6-3 6-2 win over Lukas Dlouhy and Jiri Vesely as they saved all the three break chances.
They broke the Czech team thrice, racing to the win in just 59 minutes.
Bopanna and Mergea next face next 14th seeds Treat Huey and Max Mirnyi, who beat Brazilians Thomaz Bellucci and Marcelo Demoliner 5-7 7-6(2) 6-4.
Bhupathi's campaign ended with tame 3-6 2-6 defeat against American third seeds Bob and Mike Bryan.
Meanwhile, Leander Paes and Martina Hingis' mixed doubles match against Russia's Anastasia Pavlyuchenkova and Dominic Inglot from Britain was cancelled due to rain.
