Rasool made a strokeful unbeaten 101 that came off 167 balls and was studded with eight boundaries and three sixes to single-handedly take Jammu and Kashmir to a respectable total.
Besides Rasool, Ian Dev Singh made 47 while opener Adil Reshi scored 45.
Asked to bat, Jammu and Kashmir lost their first wicket in the form of Shubham Khajuria (8) at the team score of 41 in 11.1 overs.
But Jammu and Kashmir witnessed another mini collapse when they lost four wickets by adding just 61 runs.
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Rasool, on the other hand, stood like a rock and played a captain's knock to hold Jammu and Kashmir's innings together.
For Himachal Pradesh, Rishi Dhawan (3/98) picked up three wickets Akash Vasisht (2/59) scalped two.
Brief Scores:
Jammu and Kashmir: 274 for eight in 90 overs (Parvez Rasool 101 not out; Rishi Dhawan 3/98).