The Indo-Sweden pair of Bhupathi and Lindstedt lost 6-2 3-6 8-10 to Daniel Gimeno-Traver of Spain and Paolo Lorenzi of Italy in just 59 minutes.
It was Bhupathi's first tournament after US Open, where he was knocked in the first round along with German partner Philipp Petzschner.
The Indian challenge is still alive in the tournament as Leander Paes is also playing in the doubles event. Paes and his Italian partner Daniele Bracciali have been seeded second and they will open their campaign against James Cerretani and Adil Shamasdin.
The Indian lost 3-6 3-6 to his lower-ranked Italian rival after one hour and 15 minutes. While Somdev is ranked 98, Viola is 140 on the ATP ranking charts. It was first meeting between the two players.
Somdev's fifth double fault of the match handed Viola two match points. The Indian saved first but Viola converted second to set up a second round clash with world number four Spaniard David Ferrer.