In reply, Tripura were 118 for two in 42 overs at stumps with opener Udiyan Bose retiring hurt on 52.
Tripura still trail Kerala by 229 runs in their quest for the vital first innings lead.
Earlier resuming at the overnight score of 223 for four, Prem, batting on 94 last evening, completed a fine century that came off 264 balls. He struck eight boundaries and two sixes.
Rana Dutta (5/50) picked up a five-wicket haul for Tripura.
Brief Scores:
Kerala: 347 all out in 129.5 overs (Rohan Prem 118, Sachin Baby 70; Rana Dutta 5/50).
Tripura: 118 for two in 42 overs (Udiyan Bose 52 retired hurt; S Sandeep Warrier 1/34).
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