Resuming at the overnight score of 118 for one in reply to HP's 338-run first innings total, Goa were 347 for eight at stumps on the third and penultimate day of the encounter.
Pinto's unbeaten knock came off 180 balls with the help of six fours and a six, while Asnodkar faced 242 deliveries and struck nine boundaries during his stay.
Apart from Pinto and Asnodkar, Amogh Sunil Desai scored a fine 59 off 141 balls. He hit 10 boundaries in the process.
At stumps, Harshad Gadekar (2) was giving Pinto company at the crease.
For HP, Rahul Singh scalped four wickets for 71 while pacer Vikramjeet Malik and leg-spinner Karanveer Singh picked up two wickets apiece.
Brief Scores:
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Himachal Pradesh 1st innings: 338 all out in 126 overs (Amit Kumar 86, Mukesh Sharma 73; Gauresh Gawas 4/109).
Goa 1st innings: 347 for eight in 142 overs (Reagen Pinto 85 not out, Swapnil Asnodkar 81; Rahul Singh 4/71).