Tamil Nadu now need 126 more runs with four wickets in hand to overtake Uttar Pradesh's first innings total of 524.
At the close of play, Indrajith was unbeaten on a solid 70 and giving him company at the other end was A Aswin Crist on 2.
Earlier, starting the day on 34 for one, overnight batsman Mukund, resuming at a personal score of 18, went on to put up a dominating show with the bat and complete his century.
Tamil Nadu captain shared a solid 132-run stand for the fourth wicket with Karthik, whose 121-ball 73 included 11 hits to the fence and another 50 runs with Indrajith for the fifth wicket.
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Brief scores:
Uttar Pradesh 1st innings: 524
Tamil Nadu 1st innings: 398 for six in 110 overs (Abhinav Mukund 154, Dinesh Karthik 73, Baba Indrajith 70 batting; Ankit Rajpoot 2/91).
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