In a match of 1 hour 53 minutes, Bopanna with his Danish partner Frederik Nielsen beat 16 seeded Radek Stepanek and Nenad Zimonjic 6-3, 6-7, 6-3, in the first round on 31 August. They will now face the US-New Zealand combination of Brian Baker and Marcus Daniell for a place in the quaterfinals.
Seventh-seeded Sania Mirza and her Czech partner Barbora Strycova beat the American pair of Jada Myii Hart and Ena Shibahara by 6-2, 6-3.
Veteran Leander Paes and Martina Hingis secured a 6-3, 6-2 win against Americans Sachia Vickery and Frances Tiafoe. The Indo-Swiss pair took just 51 minutes to beat their opponents.
However, French Open champion Garbine Muguruza and Wimbledon runner-up Milos Raonic crashed out as Novak Djokovic was handed a free pass into the last 32.
Third-seeded Spaniard Muguruza was beaten by world number 48 Latvia's Anastasija Sevastova 7-5, 6-4. Meanwhile, 120 seeded Ryan Harrison of US beat 5 seeded 6-7, 7-5, 7-5, 6-1.
26-year-old Sevastova will now face Kateryna Bondarenko.