Desai and Mansur Bisla (21) were at the crease when the play ended.
Goa, who were asked to bat after the visitors won the toss, lost an early wicket of debutant Balekar(6), who was bowled by Arup Das with the total on ten.
Kamat and Desai then took control of the situation and went on to add 155 runs for the second wicket before the former was caught by Dheeraj Jadhav off Arlen Konwar.
Desai, who retired hurt when on 65 after he got a nasty blow on his fingers from Diraj Goswami, came back to score his maiden ton with the help of eleven fours and a six. It came off 230 balls.
The visitors, who toiled hard, got rid of the well-settled Regan Pinto when he was caught by Siva Shankar Roy off Syed Mohammed for 61.
Regan's fifty came with the help of five fours and a six in 96 balls.
For the visitors, Das, Konwar and Syed Mohammed claimed a wicket each.
Brief scores:
Goa 1st innings: 264/3 in 90 overs (Amogh Desai batting 101, Sagun Kamat 70, Regan Pinto 61).
