Rutuja carved out a creditable 6-2 4-6 6-3 in four minutes over two hours over the sixth-seeded Sai Samhitha and led six others into the quarter finals.
Two service breaks helped Rutuja grab the first set before Sai recovered to win the second with a break of serve in the ninth.
In the decider, Rutuja recovered from the lapse of concentration to play steadily and decisively break Sai in the 9th game before winning the set and the match.
Second seed Xiaoxi Zhao of China was the lone foreign entrant in the last eight.
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In the pre-quarterfinals, left-handed Ramya breezed past Sindhu Janagam 6-0 6-2, Shweta led 5-0 before eighth seeded Australian Alexandra Walters retired due to exhaustion, while Yubarani accounted for another youngster Vasavi Ganeshan 6-3 6-3.
Seventh-seeded Pranjala Yadlapalli, a semi finalist here last year, got past young German rival Vivien Klein 6-0 6-3 while another teen, Mahak, played matured tennis to rally past Britain's Manisha Foster 7-5 6-4 in a well-contested match.
China's Xiaoxi halted the run of wild card Snehal Mane, winning 6-4 6-1.
Other results: Doubles (Quarter finals): 4-Manisha Foster (GBR)/Alexandra Walters (AUS) bt Kaaviya Balasubramanian /Shivani Manjanna (IND) 6-1 6-2; 3-Pranjala Yadlapalli (IND)/Xiaoxi Zhao (CHN) bt Snehal Mane (IND)/Hsin-Yuan Shih (TPE) 6-2 6-1.
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