Reduced to 46 for 3 overnight while chasing a mammoth 477, Assam's chances of sneaking away even with a draw were slim but Tarjinder fought all through before becoming the last wicket to fall after making 105 runs.
This was J&K's first win of the season and Parvez Rassol had a massive role to play in it top-scoring in both innings with 67 and 120 not out and taking seven for 41 in Assam's first innings.
In Assam's second innings, six visiting bowlers were among the wickets with Ram Dayal taking three.
Apart from Tarjinder's hundred, which came off 187 balls and included 12 fours and a six, the only other knock of significance in the Assam scoresheet was by skipper Dheeraj Jadhav.
Jadhav scored patient 51 runs which came off 135 deliveries and included eight fours.
No other Assam batsman could make any worthwhile contribution with six of them failing to touch doubles figures, including four ducks.
Jammu and Kashmir: 323 & 318 for 5 declared.
Assam: 165 & 241 all out in 89.1 overs (Tarjinder Singh 105; Ram Dayal 3/50).