Hope scored his fourth century of a prolific tour, ending up unbeaten on 102 off just 50 balls, with four fours and nine sixes and reaching the milestone with a six off the final delivery of the West Indies innings as they finished on 3-247.
It was the third time he had scored an unbeaten century in a white-ball international against India in 11 days - and just like the previous two occasions, the West Indies emerged victorious.
Hope's third T20I century, the most for any West Indian batter and taking him past 2000 runs in the format, helped his side amass the second-highest first innings total in T20s against India, trailing only England's 3-257 in Southampton this year.
Chasing 248, India made a brisk start with Sanju Samson racing to a half-century off 20 deliveries before falling to Keemo Paul for 56 but they were eventually bowled out for 223.
Shreyas Iyer had chipped in with 16 off 11 balls and Abhishek Sharma contributed 29 before Gudakesh Motie removed the opener.
India then accelerated again at the death through Nitish Kumar Reddy and Tilak Varma, who added 70 from 32 balls to keep the chase alive, but Varma fell for 43 and Reddy was dismissed by Keemo Paul, who triggered a collapse by claiming three wickets in the 19th over.
West Indies, put in to bat, had made a brisk start with Jewel Andrew providing early impetus alongside Hope before Axar Patel trapped the opener lbw for 21 off 16 balls.
Shimron Hetmyer and Hope added a rapid 58, but Prince Yadav broke the stand with a caught-and-bowled effort to dismiss Hetmyer for a blistering 33 off 12 balls. Rovman Powell followed soon after, departing for 24.
Hope remained unfazed, however, sharing an unbroken 91-run stand from 43 balls with Sherfane Rutherford who finished unbeaten on 49 off 26 deliveries.
