Starting the day on 96 for one, Kerala rode on overnight batsman Hegde, who resumed on 52, Amit Verma (42) and Prem's crucial knocks to cross 300-run mark and take a huge first innings lead.
While Hegde's innings came off 209 balls, studded with 12 fours, Prem took 91 deliveries for his 58 that included seven boundaries.
Tripura, who were bundled out for a meagre 179 in their first innings, did not have an ideal start to their second essay also as they lost two wickets in 34.3 overs.
At stumps, Tripura were still tailing by 38 runs with eight wickets in hand with opener Bishal Ghosh unbeaten on 47.
Brief scores:
Tripura: 179 & 84 for 2 in 34.3 overs (Bishal Ghosh 47 not out).
Kerala: 301 for 9 decl. In 109.3 overs (Abhishek Hegde 82, Rohan Prem 58, Amit Verma 42; Rana Dutta 4/45).
