Having started the day on 284 for four, overnight batsman Yashpal Singh, who resumed on 92, scored an unbeaten ton to take the team past 470-run mark. He also put on three crucial partnerships with different batsmen in the entire day.
After Services lost the other overnight batsman, Rajat Paliwal and Nakul Verma (1) early on the day, Yashpal and Khalid consolidated the visitors' innings.
Paliwal, who started on 23, though could add just 19 runs more today before he fell for a well-made 42 off 85 balls, studded with six boundaries, his fifth wicket stand with Yashpal yielded 83 runs.
Yashpal and Khalid put on a 62-run together for the seventh wicket before the former shared another fruitful partnership of 71 runs for the ninth wicket with Suraj Yadav.
Khalid hit 86-ball 35 and Suraj scored 45 off 72 balls.
Yashpal held fort till he ran out of partners at the other end to remain stranded at an unbeaten 166 off 313 balls, laced with 14 fours and a six. He spent 497 minutes at the crease.
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For Goa, Shadab Jakati was the pick of the bowlers with four for 100.
In reply to Services' huge first innings total, Goa lost opener Sagun Kamat for 28.
When stumps were drawn, Swapnil Asnodkar was batting on 17 and Amogh Desai was not out on 16.
Brief scores:
Services: 473 all out in 153 overs (Yashpal Singh not out 166, Soumik Chatterjee 103; Shadab Jakati 4/100, Saurabh Bandekar 3/101).
Goa: 64 for one in 27 overs (Sagun Kamat 28; Avishek Sinha 1/10).