Bopanna and his Canadian partner Gabriela Dabrowski had to dig deep to beat Michael Venus and Katarina Srebotnik 6-4 6-7, 10-7 in a super tie-breaker.
A little later, the second-seeded pairing of Mirza and Croatia's Ivan Dodig got the better of reigning defending US Open defending champions, Laura Siegemund and Mate Pavic, in another first round match.
The final scoreline read 7-5, 6-4. While the Indian challenge in the men's doubles has already ended with the exit of Bopanna and Leander Paes, Mirza still remains in the contention in the women's doubles partnering Czech Republic's Barbora Strycova.
The fourth seeds eased past the Australian-Chinese pair of Samantha Stosur and Shuai Zhang in a second round match yesterday.
In other matches of Indian interest today, Siddhant Bhatia lost his first round boys' singles match against Australia's Alexander Crnokrak 6-2, 6-7, 5-7.
However in the girls' singles first round, Zeel Desai overcame a stiff challenge from local hope Kaitlin Staines 6-4, 3-6, 7-5.