The Indian wild card lost 3-6 0-6 to her opponent in the second round of the USD 125,000 at the Shiv Chattrapati Sports Complex, Balewadi.
The 16-year-old, playing in her maiden WTA event, was no match to her opponent's powerful groundstrokes and deceptive drops.
The 2011 national champion Rutuja had registered an upset victory in the opening round of the tournament against So-Ra Lee.
Svitolina broke Rutuja's serve in the sixth game and then eased through the set before raising the bar high in the second set that Rutuja could not match her rival.
In the other matches, third seed Donna Vekic of Croatia was made to work hard for victory by Oksana Kalashnikova of Georgia before winning 6-2, 4-6, 6-0, while fourth seed Eva Birnerova of Czech Republic was shown the door by Thailand's Luksika Kumkhum 3-6, 6-3, 6-1.
Results (2nd round):
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Singles: 3-Donna Vekic (CRO) bt Oksana Kalashnikova 6-2, 4-6, 6-0;
Luksika Kumkhum (THA) bt 4-Eva Birnerova (CZE) 3-6, 6-3, 6-1;
Elina Svitolina (UKR) bt Rutuja Bhosale (IND) 6-3, 6-0
Doubles:
Yi-Fan Xu/Yi-Miao Zhou (CHN) bt 3-Monique Adamczak/Stephanie Bengson (AUS) 6-3, 6-2.