At stumps, Misal was unbeaten on 67 and giving him company at the other end was Amit Yadav on eight.
Put in to bat, opener Desai hit a superb 75 off 114 balls studded with 11 fours to provide a solid platform to Goa. During his knock, he also put on 92 runs for the opening wicket with skipper Swapnil Asnodkar (14).
One-down batsman Sagun Kamat (41) also chipped in with important runs.
For Kerala, Basil Thampi (3/97) and Nizar Niyas (2/60) shared five wickets between them.
Brief scores:
Goa 1st innings: 313 for six in 89 overs (Amogh Desai 75, Darshan Misal batting 67, Saurabh Bandekar 60; Basil Thampi 3/97).