Chasing 224 for victory in Indore, West Indies suffered an early setback when Arshdeep Singh dismissed captain Shai Hope for five after he missed a swipe at a delivery that jagged back on to his stumps.
Shimron Hetmyer kept the visitors in the hunt with a brisk 43 off 26 balls before spinner Naman Dhir broke the stand, while Axar Patel removed Rovman Powell to leave West Indies struggling to match the mounting required rate.
Quentin Sampson and Sherfane Rutherford briefly revived the chase, but West Indies could not sustain the momentum as wickets fell regularly in the closing overs and they finished on 7-209.
Arshdeep was India's standout bowler with 3-44 as the hosts defended a formidable 223 after being asked to bat.
India recovered from the early loss of Sanju Samson, who fell for just three to Shamar Joseph, through a 108-run partnership for the second wicket between Abhishek Sharma and Ishan Kishan.
Sharma dominated the scoring with an explosive 69 off 30 balls, while Kishan contributed 37. However, the hosts lost momentum when Kishan's dismissal triggered a middle-order collapse.
The platform laid by Sharma ultimately proved decisive, allowing the lower order to keep the scoreboard moving and lift India to 223 before they were bowled out off the final delivery of the innings.
The teams meet again in the fourth Twenty20 International in Hyderabad on Wednesday.
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