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.
Odisha skipper Govinda Poddar (29) played confidently and helped Behera add 48 runs before throwing it away. His attempt to whack off-spinner M S Washington Sundar saw a mishit fall into the hands of Abhinav Mukund.
On a slow wicket, Tamil Nadu bowlers found the going tough but two more quick strikes raised their hopes.
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.
Biplab Samantaray (44 batting) and Shantanu Misra (37 batting) forged an unbeaten 78-run stand for the fifth wicket and more importantly played out 30 overs at a time when the Tamil Nadu bowlers were on the look-out for wickets.
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.
Brief scores: Tamil Nadu 530 for 8 declared in 165 overs (Murali Vijay 140, Vijay Shankar 100, B Aparajith 109 not out, B Indrajith 46, Suryakanth Pradhan 3 for 75) vs Odisha 286 for 4 in 101 overs (Natraj Behera 91, Sandeep Pattanaik 66, Biplab Samantaray 44 batting, M S Washington Sundar 2 for 48).
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).
At Mumbai: Mumbai 171 all out in 56.2 overs (Aditya Tare 50, Atit Sheth 5 for 50, Lukman Meriwala 5 for 52) and 102 for 4 in 29 overs (Prithvi Shaw 56, Ajinkya Rahane 28 batting) vs Baroda 575 for 8 declared in 180 overs (Swapnil K Singh 164, Aditya Waghmode 136, Deepak Hooda 75, Shardul Thakur 3 for 95).
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)