Seeded seventh, Rashmi had to endure anxious moments in the decider before winning the third set tie-breaker 11-9 to set up a semi-final clash with second seed Sharrmada Baluu of Karnataka, who brushed aside Delhi's Shweta Rana 6-2 6-1.
In another upset victory, unseeded Nandini Sharma of Punjab sent the fourth seed from West Bengal, Amrita Mukherjee, packing with a 4-6 6-4 6-2 victory.
There was an upset in the men's second round matches too, with AP's Sai Saran Reddy getting the better of his sixth seeded state mate Shaikh Abdullah 6-4 7-6 (3).
Top seed Mohit Mayur of TN and 3rd seed Anvit Bendre of Maharashtra booked their spots in the quarter-finals without much ado.
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Results:
Women's Singles (Quarter finals): 1-Natasha Palha (Goa) bt Baburaj Nityaraj (TN) 6-3 6-3; 7-Rashmi Teltumbde (MAH) bt 3-Sai Samitha C (TN) 6-3 1-6 7-6 (9); 2-Sharrmada Baluu (KNT) bt Shweta Rana (DEL) 6-2 6-1; Nandini Sharma (PUN) bt 4-Amrita Mukherjee (WB) 4-6 6-4 6-2.