The 97th-ranked Somdev saved as many as nine break chances before losing 6-7(6), 3-6 in an hour and 34 minutes.
Somdev traded a break with Verdasco to push the opening set to the tie-breaker.
In the second set, he saved two of three break chances but that one chance was enough for Verdasco to seal victory.
In the doubles, Bhupathi failed to cross the first round for the third successive time as he and his Swedish partner Robert Lindstedt were beaten in straight sets by Serbia’s Novak Djokovic and Switzerland’s Stanislas Wawrinka.
Seeded second, Bhupathi-Lindstedt lost 3-6, 3-6 in 63 minutes.
Bhupathi had suffered first round defeats at the US Open and in Bangkok.
India's challenge in the event is still alive as top seeds Leander Paes and his Canadian partner Daniel Nestor face Americans John Isner and Sam Querrey.
Image: Somdev Devvarman
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