At the draw of stumps, Goa were 118 for one in their first innings with opener Swapnil Asnodkar and Amogh Desai batting on 64 and 31, respectively.
Resuming the day from 210 for five, Himachal added another 128 runs thanks to the eighth wicket stand of 86 runs between Karanveer Singh and Rahul Singh.
Karanveer scored an unbeaten 39 while Rahul made 47.
For Goa, debutante Gaurish Gawas was the most successful bowler, claiming four wickets for 109 runs, while Shadab Jakati took three for 78.
