Etee will take on compatriot Natasha Palha in her first ever quarter-finals in an ITF Women's event.
Overall, it was a good day for India a six of the eight quarter-finalists are from the host nation but the bad news was that top seed and Olympic hopeful Prerna Bhambri had to concede her match due to a shoulder injury.
Prerna was trailing 0-4 in the first set when she opted out of the match against Poojashree Venkatesha.
Meanwhile, S Peddi Reddy recovered from a second set lapse to beat qualifier Simran Kaur Sethi 6-4 0-6 6-4 in a well-fought second round match.
Simran's Junior Fed Cup teammate Rutuja Bhonsle was no match for Lee Pei Chi of Taipei as she went down in straight sets 6-3 6-3.
Palha continued her fine run in the event with a hard fought win over compatriot Shweta Rana 4-6 6-2 6-3.
Ratnika Batra also advanced with a 6-1 6-4 win over Ambika Pande while Sharmada Balu routed Hong Kong qualifier Ho Ching Wu 6-0 6-1.
