While Chitra defeated Hong Kong's Yu Ching 3-1, Neena put paid to the hopes of Russia's Irina Gorbataya by an identical margin.
Varshaa, who became the first Indian to qualify for the next round, also came up triumphant in her last league match, outclassing Ukraine's Maria Buckaraska 3-0.
In the men's section, Manan Chandra continued his impressive run with another victory even as his other countrymates fell by the wayside.
Khan went down 2-4 against Brenden O'Donoghue of Ireland and Damani was tamed by Germany's Roman Dietzel with an identical scoreline.
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In the masters section (above 40), S A Saleem bowed out of the competition after losing 2-3 to Ian Sergeant from Wales.
Nigel Lazar, too, lost to Murat Ayas 1-3.
Results:
Men's: Manan chandra bt Tomaz Skalski (Belgium) (4-2) 75-44 0-88 46-56 80-17 82-14 51-7.
Shahbaaz Adil Khan lost Brenden O'Donoghue (Ireland): (2-4) 72-50 16-68 88-6 56-25 33-61 71-15.
Women's: Chitra M bt Yu Ching (Hong Kong): (3-1) 51-63 80-58 69-20 74-25.
Neena Praveen bt Irina Gorbataya (Russia): (3-1) 55-13 56-43 39-70 81-58.
Varshaa Sanjeev bt Maria Buckaraska (Ukraine): (3-0) 65-47 48-2 53-40.
Masters: Nigel Lazer lost Murat Ayas: (3-1) 75-24 62-48 33-55 60-53.
S A Saleem lost Ian Sergeant (Wales): (3-2) 51-74 27-65 63-62 0-97 0-97.