Resuming the day at 281 for eight, Goa could only add 36 more runs before being bowled out at the Sher-i-Kashmir Stadium.
Ram Dayal turned out to be the most successful bowler for J&K with figures of five for 85.
In response, Adil Rishi (80) and Manzoor Dar (58) scored half-centuries to help J&K reach near the 300-run mark.
Apart from Rishi and Dar, wicket-keeper Obaid Haroon and Manik Gupta made identical scores of 33.
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Brief Scores:
Goa 1st innings: 317 all out in 97.1 overs (Keenan Vaz 99, Saurabh Bandekar 64 not out; Ram Dayal 5/85).
Jammu and Kashmir 1st innings: 282 for eight in 80 overs (Adul Rishi 80, Manzoor Dar 58; Shahdab Jakati 4/71).