In reply to Services' huge first innings total of 473, Goa batsmen, especially Ravikant Shukla and Rohit Asnodkar, showed a lot of patience to help the team cross 300-run mark.
At stumps, Ravikant was unbeaten on 78 and Rohit was batting on 52.
Resuming on 64 for one, both the overnight batsmen -- Swapnil Asnodkar, starting on 17, and Amogh Desai, on 16 -- gave the hosts a good start.
Swapnil hit a well-made 74 off 225 balls, studded with seven boundaries, Desai scored a 124-ball 40.
The duo shared a 78-run stand for the second wicket.
After Desai departed with the scorecard reading 122 for two, Goa suddenly found themselves reeling at 193 for five with a few quick wickets.
But Ravikant and Rohit consolidated Goa's innings by putting on an unbeaten 119-run stand for the sixth wicket.
Ravikant's knock came off 132 balls, laced with six fours and a six, while Rohit's 52 was scored off 135 balls, including five boundaries.
Goa, however, have an uphill task as they still trail Services by 161 runs with five wickets in hand.
Goa: 312 for five in 117 overs (Swapnil Asnodkar 74, Ravikant Shukla batting 78, Rohit Asnodkar batting 52; Yashpal Singh 2/08).