The visiting bowlers continued their fine show as they shot Himachal Pradesh out for 260 runs in 77 overs at the Atal Bihari Vajpayee Stadium.
Himachal, who began the day at 111 for five, conceded 181-run first innings lead in the Group C match.
Tripura, who had scored 441 all out in their first innings, did not enforce a follow-on on the home side and they were 116 for five in their second essay at stumps, stretching the overall lead to 297 with five second innings wickets intact.
Abbas Ali was batting on 59 while Manisankar Murasingh was giving him company on 19.
Tripura, however, suffered a top-order collapse with four of their five specialist batsmen dismissed without reaching double digit figures as the visiting side slumped to a precarious 13 for four in the seventh over.
Pacer Vikramjeet Malik took the wickets of three of the four Tripura top-order batsmen.
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Abbas Ali and Abhijit Dey (18) stopped the slide with a 71-run stand for the fifth wicket.
Earlier, Rishi Dhawan top-scored for Himachal Pradesh with a 69-ball 54 while Rahul Singh remained not out on 49 as the home side added 149 runs today after resuming at overnight 111 for five.
Brief Scores:
Tripura: 441 and 116 for 5 in 48 overs (Abbas Ali 59 batting; Vikramjeet Malik 3/25).
Himachal Pradesh: 260 all out in 77 overs (Rishi Dhawan 54; Rana Dutta 4/65).