Resuming the day on 225 for 5, Tamil Nadu added 292 runs from 91 overs and lost just two wickets as the visiting side bowlers were sent for a leather hunt at the the Emerald High School Ground here.
Kousik and Rangarajan put on 196 runs for the seventh wicket, after Prasanna was caught behind for 70 off Udit Birla in the 17th over of the day.
Rangarajan, who remained unbeaten on 124 at close, faced 226 balls and hit seven fours and three sixes.
Aswin Crist was the other not out batsman, batting on eight when the stumps were drawn.
Brief Scores:
Tamil Nadu 1st Innings: 517/7 in 180 overs (Jagatheesan Kousik 151, Malolan Rangarajan batting 124; Udit Birla 3/46).