Sowjanya shocked no. 4 seed Emi Mutaguchi of Japan, while Rutuja ousted fifth seed Shweta Rana.
No. 2 seed Prathana Thombare and no. 8 Nidhi Chilulmula scored victories to advance to the next round, while top seed Ankita Raina, no. 3 Rishika Sunkara, no. 6 Prerna Bhambri and no. 7 Natasha Palha also made the last eight grade.
Left-handed Sowjanya from Hyderabad, ranked 702, beat 552nd ranked Japanese rival 4-6 6-2 6-1 in a two-hour and 40-minute contest.
"I'm relieved to come out as a winner. I just lost my focus midway," said Rutuja, who led 5-3 in the decider before Rana took three games in a row to go up 6-5.
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Rutuja held her serve in the 12th game to force the tie break.
Prarthana scraped past a fighting Chihiro Nunome of Japan 6-7(5) 6-2 7-6(1) in a three hour and 35-minute battle. The Indian player was leading 5-3 in the first and the third sets before clawing her way back to win the third set in the tie-break.
Results: Singles (Round 2): Ankita Raina-1 bt Damini Sharma 6-2 7-5; Prerna Bhambri-6 bt Akshara Iska 6-2 6-0; Sowjanya Bavisetti bt Emi Mutaguchi-4 (Jpn) 4-6 6-2 6-1; Rutuja Bhosale bt Shweta Rana-5 6-1 0-6 7-6(8-6); Nidhi Chilumula-8 bt Bhuvna Kalva 7-6(5) 6-4; Rishika Sunkara-3 bt Amrita Mukherjee 6-2 6-2; Natasha Palha-7 bt Shrishti Slaria 6-2 6-0; Prarthana Thombare-2 bt Chihiro Nunome (Jpn) 6-7(5) 6-2 7-6(1).