Himachal restricted J & K to 133 for the loss of five wickets and then chased down the target with 11 balls to spare.
Opting to bat, J & K's young all-rounder Parveez Rasool top-scored with an unbeaten knock of 44. It was Rasool's unbeaten partnership of 36 runs for the sixth wicket with Nadeem Dar that helped the team reach a respectable total after struggling at 97 for five at one stage.
Off-spinner Gurvinder Singh was the best bowler for Himachal, returning impressive figures of 3 for 18.
Dogra, alongwith Vikramjit Malik (30), stabilised the innings with a 33-run partnership for the second wicket before Malik was trapped in front by Rahil Sambyal.
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Dogra's knock of 50 came off 44 balls and was studded with five fours and two sixes.
Dogra shared a 64-run partnership with Amit Kumar (21) for the third wicket and took Himachal closer to victory, before Dhruv Singh (12) completed the task in the 19th over.
Brief scores: Jammu & Kashmir 133/5 in 20 overs (Parveez Rasool 40, Shubham Khajuria 28, Gurvinder Singh 3/18).