The majority of the opening day's play in the four-day game was lost due to wet conditions after rain delayed the start of the match.
The star-studded batting line-up of the visitor's had to toil hard for runs and it was evident from the pace of scoring of openers Abhibnav Mukund and Murali Vijay, who putting on 37 runs for the first wicket off 20.2 overs in 108 minutes.
Vijay managed only 15 in a cautious effort before he was caught by Rakesh Mohanty off Alok Mangaraj. S Badrinath was the other Tamil Nadu batsmen to get out for 11, bowled by Basant Mohanty.
Mukund was unbeaten on 21 at stumps and giving him company was Baba Aparijith on three.
For Odisha, Basant Mohanty (1/26) and Mangaraj (1/21) picked up one wicket each.
Brief scores:
Tamil Nadu: 66 for 2 in 31 overs (Abhinav Mukund batting 21, Murali Vijay 15; Basanta Mohanty 1/26, Alok Mangaraj 1/21).