At stumps, opener Sibsankar Roy was unbeaten on 48, while Amit Sinha was batting on 2 at the District Institute of Education and Training Ground.
Amogh Sunil Desai (105) Reagan Pinto (61) were the main contributors for Goa.
For Assam, medium pacer Arup Das returned figures of five for 83.
At the end of day's play, Assam trailed the hosts by 247 runs with nine wickets remaining.
Goa were 264 for three overnight.
Brief scores:
Goa 1st innings: 381 all out in 134.5 overs (Amogh Sunil Desai 105, Reagan Pinto 61, Manvinder Bisla 48; Arup das 5/83)
Assam 1st innings: 134 for one in 43 overs (Pallavkumar Das 70, Sibsankar Roy batting 48).
