Openers Natraj Behera and Sandeep Pattanaik, resuming at 36 for no loss, frustrated the Tamil Nadu attack with a century stand.
They mixed defensive play with attractive strokes to keep the scoreboard moving in respose to the visiting team's 530 for 8 declared.
Yomahesh provided the breakthrough for the visitors when he got Pattanaik, caught by substitute Kaushik Gandhi after the openers had put on 136 runs.
On a slow wicket, Tamil Nadu bowlers found the going tough but two more quick strikes raised their hopes.
More From This Section
Subhransu Senapati, who walked in after the fall of Poddar, didn't last long and was castled by Sundar for 4.
Behera missed out on a well-deserved century when he was trapped leg-before by Rahil Shah to leave Odisha at 208 for 4.
His knock of 91 contained 13 fours and a six.
Sundar was the most successful Tamil Nadu bowler, finishing with two wickets for 45 while Yomahesh and Shah scalped one each.
With just a day's play left, Tamil Nadu's chances of posting an outright win have been dented with the home team's batsmen showing great resolve on a docile pitch.
Tamil Nadu had made 530 for 8 before declaring its first innings riding on tons by Murali Vijay, B Aparajith and Vijay Shankar.
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) and 51 for 1 in 17 overs (Prashanth Kumar 29) vs Tripura 315 all out in 99.4 overs (M B Mura Singh 81, Gurinder Singh 81, S M Singha 39, Bhargav Bhatt 4 for 93).