Andhra also earned a bonus point for their efforts.
Medium-pacer Shivkumar took four wickets to run through Tripura, who had a 16-run first-innings lead.
Resuming on 20 for three, Tripura could add just 66 runs to their second innings total, leaving Andhra a fourth-innings chase of a mere 103 runs.
Andhra took 21.2 overs to achieve the target with the openers remaining unbeaten.
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Brief scores:
Tripura: 179 & 86 (Duvvarapu Shivkumar 4/24)
Andhra: 163 & 104 for no loss (Srikar Bharat not out 64, Prasanth Kumar not out 39).