Ahmedabad-born Ankita, the eighth seed with a world ranking of 315, was beaten 6-4 6-3 in an hour by her left-handed Ukrainian rival, who is 174 in the latest rankings, to bring an end to the host country's challenge in singles event at the Cricket Club of India courts.
Vasylyeva will meet Slovokian Tadeja Majeric, who defeated sixth seeded Ukrainian Sofiya Kovalets 6-4 6-7 (10-8) 6-3.
There was an upset when unseeded Emily Webley Smith of Britain toppled top seed Patricia Mayr-Achleitner of Austria in a nail-biting three setter.
Results:
Singles (Quarterfinals): (3) Marina Melnikova (RUS) bt Ho Chin Wu (HKG) 6-0 6-2; (2) Anastasiya Vasyleva (UKR) bt (8) Ankita Raina (IND) 6-4 6-3; Emily Webley-Smith (GBR) bt (1) Patricia Mayr-Achleitner (AUT) 6-7 6-2 7-5; (4) Tadeja Majeric (SLO) bt Sofiya Kovalets (UKR) 7-5, 7-5.