Kohli struck seven maximums in a blistering unbeaten knock of 70 off 29 balls, while KL Rahul (91 off 56 balls) and Rohit Sharma (71 off 34) shared nine of their own as India racked up 240-3 off their 20 overs.
Rahul and Sharma set the platform for India’s massive score with an opening stand of 135 before Rahul and Kohli added 95 for the third wicket after Rishabh Pant fell without scoring.
In reply, the twice T20 world champions finished on 173-8 after slumping to 17-3 with captain Kieron Pollard top-scoring with 68 from 39, his innings featuring six sixes and five fours.
The tourists had to make do without the power-hitting of opener Evin Lewis, who was unable to bat after suffering soft tissue damage to his right knee while fielding.
Shimron Hetmyer, who made 41 off 24, and Pollard added 74 for the fourth wicket to give West Indies some hope before left-arm wrist-spinner Kuldeep Yadav (2-45) dismissed the former.
Kuldeep also removed Jason Holder before Pollard holed out at wide long on off seamer Bhuvneshwar Kumar (2-41).
The teams will now contest three one-day internationals, the first of which takes place at Chennai on Sunday.