Electing to bat, the visitors lost skipper Abhinav Mukund (12), who was run-out following a mix-up with Vijay.
However, the Test opener was involved in two century partnerships, first with wicket-keeper N Jagadeesan (88) and B Indrajith (41 batting), which put Tamil Nadu in the driver's seat.
After a cautious start, Vijay came into his own, playing a series of beautiful shots and reached his hundred in a hurry from the mid-80s with a huge six.
He didn't miss out on an opportunity to score and crunched some boundaries while Vijay played himself in.
The partnership between Vijay and Jagadeesan yielded 145 runs before the latter fell to Odisha captain Govind Poddar, 12 short of a ton.
Vijay took over after Jagadeesan's exit and dominated a 118-run stand with Indrajith.
A streak of aggression took him to a century from the 80s as he looked to step up the run-rate.
He fell late in the day, caught and bowled by Suryakanth Pradhan, who was the host team's best bowler, bagging 1 for 48 from 16 overs.
Indrajith (41) and all-rounder Vijay Shankar (eight) were at the crease when stumps were drawn.
Brief Scores: Tamil Nadu 292 for 3 in 90 overs (Murali Vijay 140, N Jagadeesan 88, B Indrajith 41 batting) vs Odisha.
At Agartala: Andhra 252 for 2 in 89.6 overs (D B Prashanth Kumar 120 batting, G Hanuma Vihari 62, Ricky Bhui 49 batting) vs Tripura.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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