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India chased down the target of 165 with six balls to spare with Suryakumar Yadav top-scoring with a 44-ball 76. Rishabh Pant remained not out on 33 off 26 balls.
For West Indies, Akeal Hosein, Dominic Drakes and Jason Holder took a wicket apiece.
India had won the first T20I by 68 runs before losing the second match by five wickets.
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Opener Kyle Mayers top-scored for the West Indies with a 50-ball 73 while Rovman Powell contributed 23.
For India, Bhuvneshwar Kumar took two wickets for 35 runs while Hardik Pandya and Arshdeep Singh got one each.
Brief Scores: West Indies: 164 for 5 in 20 overs (Kyle Mayers 73, Rovman Powell 23; Bhuvneshwar Kumar 2/35).
India: 165 for 3 in 19 overs (Suryakumar Yadav 76, Rishabh Pant 33 not out; Akeal Hosein 1/28).