Pillai overcame Neena Praveen, also of Tamil Nadu, 3-1, while Sanchis defeated giant-killer Suniti Damani (West Bengal) 3-0 in the semi-finals.
Sanchis played a crafty game as she repeatedly snookered Damani, who had earlier shocked last year's runner-up Meenal Thakur (Maharashtra) in the quarter-finals, and came out a comfortable winner.
Pillai yet again lost the first frame, but bounced back strongly like she had done against Chitra Magimairaj (Karnataka) in the quarter-finals when she trailed 0-2.
Earlier, the 31-year-old Damani caused a big upset by knocking out Thakur 3-0 en route to the semi-finals.
Winner of the national nine-ball pool championship this year, Damani capitalized on the errors by Thakur who just could not get into the flow.
Meanwhile, Pillai, the 33-year-old from Chennai, came back from two frames down to beat Magimairaj 3-2 in a tense match.
The turnaround for Pillai came in the third frame when Magimairaj missed a yellow after potting the last red and the follow black. Pillai pounced on the opening for a break of 20 to take the frame.
In the fourth, Pillai crafted a run of 33 in her second visit to level at 2-2 to push the match into the deciding fifth frame that she eventually won on the last black.
Magimairaj missed the last pink when ahead and Pillai took the colour followed by the black to tie the score. Pillai subsequently took the re-spotted black after a bout of safety play to clinch the issue.
In the other two quarter-finals, Praveen was taken to five frames by young Keerath Bhandaal of Delhi while Sanchis got past billiards champion Umadevi Nagaraj (Karnataka) 3-1.
The Results: Semi-finals: Vidya Pillai (TN) bt Neena Praveen (TN) 3-1 (30-57, 60-49, 57-16, 60-17); Arantxa Sanchis (Mah) bt Suniti Damani (WB) 3-0 (42-14, 70(31)-02, 72-42(23)).
Quarter-finals: Neena Praveen bt Keerath Bhandaal (Del) 3-2 (17-55, 54-34, 56-44, 20-62, 56-26); Vidya Pillai bt Chitra Magimairaj (Kar) 3-2 (45-60, 34-44, 44-36, 54(33)-17, 42-35); Arantxa Sanchis bt Umadevi Nagaraj (Kar) 3-1 (71(31)-51, 61-40, 20-71, 67-23); Suniti Damani bt Meenal Thakur (Mah) 3-0 (47-32, 39-27, 52-13).
Pre-quarter-finals: Chitra Magimairaj bt Asha (TN) 2-1; Uma Devi Nagaraj bt Heena Khandelwal (Mah) 2-0; Vidya Pillai bt Ashwini Puranik (MP) 2-0; Meenal Thakur bt Neeta Sangavi (Mah) 2-1; Neena Praveen bt Saniya Arif (Chd) 2-0; Keerath Bhandaal (Del) bt I Lahari (AP) 2-0; Arantxa Sanchis bt Indira Gowda (Kar) 2-0; Suniti Damani bt Varsha Sanjeev (Kar) 2-0.