Showing a lot of fire and spunk, Eetee played agressively to make look Kyra ordinary.
Both players were broken twice in the first set but finally Eetee held her serve at 4-4 and closed the set.
There was no stopping Eetee after the first set asshe went on to win the second set quite easily against an error-prone Kyra.
In other matches, second seed Rutuja Bhosale beat Rushmi Chakravorty with ease 6-4 6-2 while third seed Rishika Sunkara had it easy against Amrita Mukherjee with a 6-0 6-3 victory.
Other seeds Ankita Raina, Prerna Bhambr, Shewta Ranai and Prarthana Thombare also entered the quarter finals.
Katherine IP from Hong Kong beat China's Chun-Yan-He to remain as the only foreigner left in the fray.
Results, Round Two (Indians unless specified): Eetee Maheta b Kyra Shroff 6-4, 6-1; Rutuja Bhosale b Rushmi Chakravarthy 6-4, 6-2; Ankita Raina b Manya Nagpal 6-3, 6-3; Katherine IP (Hong Kong) bt Chun-Yan-He (Chn) 6-3, 6-0.