Baghdatis, bothered all season by injuries, needed treatment to his back during the match. The 23-year-old also missed matches due to a wrist injury. He was ranked as high as No. 14 in April and went into the match against Granollers ranked 43rd, but will drop even lower after the loss.
"Maybe I am going to be out of the (top) 100,'' Baghdatis said, adding that he expects to climb in the rankings soon again. "I did it before and I can do it again.''
The 22-year-old Granollers won his only tour title at Houston in April, beating James Blake in the final.
The fourth-seeded Blake advanced to the second round Wednesday by defeating Germany's Nicolas Kiefer 3-6, 6-3, 6-4.
Also in the first round, Jarkko Nieminen of Finland defeated Argentina's Eduardo Schwank 6-2, 6-4, and Belgian qualifier Kristof Vliegen beat wild card entry Philipp Petzschner of Germany 6-2, 6-3.
In second round matches, sixth-seeded Russian Igor Andreev needed more than 2 1/2 hours to overcome Germany's Philipp Kohlschreiber 7-6 (6), 6-7 (0), 7-5. Benjamin Becker beat his fellow German Andreas Beck 3-6, 6-3, 6-4.
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