Resuming at an overnight score of 224 for five, Kerala lost Akshay Kodoth (35) early.But Robert (109) and Fabid (106) played superb knocks, adding 129 runs together for the seventh wicket to take the team past 360-run mark.
Robert hit eight fours and a six during his innings that came off 261 balls, Fabid played an aggressive knock off 122 deliveries that included seven sixes and eight fours.
In reply, Goa were 81 for two in 32 overs when at close of play with Amogh Desai batting on 38 and Amit Yadav on one.
The hosts have an uphill task as they are still trailing by 360 runs with just eight wickets in hands.
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Brief scores:
Kerala 1st innings: 441 (Robert Fernandez 109, Fabid Ahmed 106; Amit Yadav 4/119).
Goa 1st innings: 81 for 2 in 32 overs.