Tvesa, who won her first event as a professional two months ago in July, and Siddhi, who won at this very course last year, carded 73 each to move to five-over 147 and tied- first place.
Saaniya Sharma, winner of the 11th Leg, and Smriti Mehra, made a whopping 11-shot improvement on their first round scores to bring in 71 each, as against 82 in the opening round. Also sharing the third place with them was Gursimar Badwal (77) at 153.
The 21-year-old Tvesa may well have been the sole leader but for a crippling triple bogey on par-3 seventh hole and another bogey on eighth. She turned in three-over 39, but on the back nine she was error free with two birdies on 10th and 12th and the rest were pars for 34.
Siddhi, still two months away from her 20th birthday, dropped a bogey each on sixth and seventh and another on 11th against birdies on ninth and 10th during her 73.
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The day's best cards came from Smriti and Saaniya, whose 71 each have been the only sub-par rounds so far in the tournament.
Afshan Fatima, one of the three co-leaders after the first round, faltered in the second with a 80 that saw her drop to 10-over 154 and sixth place.
Mehar Atwal (79-78) and Gaurika Bishnoi (77-80) were tied seventh, while Trisha Sunil (82-79) was ninth and Ankita Tiwana (83-81) was 10th.
In the final round, Tvesa and Siddhi will play alongside the seasoned Smriti in the final group, while the second to last group will see Saaniya with Gursimar and Afshan.