Wild card entrants Somdev and Prakash had to dig deep to beat Americans James Cerretani and Travis Rettenmaier 5-7, 6-4, 7-5 in their opening round at Melbourne Park.
In contrast, Bopanna and his Pakistani partner Aisam-ul-Haq Qureshi squandered one set lead to lose 6-4, 1-6, 6-7(6) to South African Rik De Voest and Scott Lipsky of the United States.
Somdev and Prakash will next take on the winners of the first round match between 11th seeds Simon Aspelin and Paul Hanley and Marcos Daniel and Daniel Koellerer.
Bhupathi, who was runner up here last year with Mark Knowles, and Belarussian Max Mirnyi are seeded fourth and will open their campaign against Michael Kohlmann of Germany and Jarkko Nieminen Finland.
Leander Paes and his Czech partner Lukas Dlouhy are seeded third and will take on the Czech pair of Leos Friedl and David Skoch in the first round.