The visitors were 163 for three in their second innings with Bandeep Singh (51) and Ian Dev Singh (40) at the crease.
J&K can push for a victory from here by declaring their innings asking the hosts to begin their chase tomorrow morning.
Tripura began the day at 85 for 2 but the batting flopped as only Parvinder Singh (60) put up some resistance while others capitulated.
Brief Scores:
Jammu & Kashmir 428 and 163 for 3 in 30 overs.(Bandeep Singh 51 batting, Ian Dev Singh batting 40; Rana Dutta 2/24)
Tripura 1st innings: 224 all out in 91.3 overs.(Parvinder Singh 60; R Dayal 4/51, Umar Nazir 2/52).