The hosts reached 36 for no loss at draw of stumps.
Resuming at overnight 292 for 3, which was built on Murali Vijay's 140, Tamil Nadu consolidated their innings with Aparajith remaining unbeaten on 109 and Shankar scoring 100 runs despite losing B Indrajith for 46 early.
Aparajith, who joined Shankar, ensured that the team scored at a brisk pace and added 177 runs.
Aparajith, who raised his second century of the season studded with nine boundaries and a six, played confidently and stepped up the tempo as the side looked for quick runs.
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Young all-rounder M S Washington Sundar didn't last too long but he hit three boundaries before falling for 14 and V Yomahesh, who made a comeback to first-class cricket in the game against Mumbai, got out for a duck.
Aparajith and K Vignesh added 26 runs before the Tamil Nadu captain declared the innings.
Brief Scores: Tamil Nadu 530 for 8 declared in 165 overs (Murali Vijay 140, N Jagadeesan 88, Vijay Shankar 100, B Aparajith 109 not out, B Indrajith 46, Suryakanth Pradhan 3 for 75) vs Odisha 36 for no loss in 13 overs.
At Agartala: Andhra 402 in 144 overs (D B Prashanth Kumar 133, G Hanuma Vihari 62, Ricky Bhui 74, A K Sarkar 5 for 68) vs Tripura 68 for 1 in 33 overs (S M Singha 33 batting).