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.
Shreyas Iyer chipped in with 16 off 11 balls and Abhishek Sharma contributed 29 before Gudakesh Motie removed the opener. India accelerated again at the death through Nitish Kumar Reddy and Tilak Varma, who added 70 runs from 32 balls to keep the chase alive.
Varma fell for 43 and Reddy was dismissed by Keemo Paul who triggered a collapse by claiming three wickets in the 19th over. India's tail folded quickly and the hosts were bowled out for 223.
West Indies, put in to bat, made a brisk start with Jewel Andrew providing early impetus alongside captain Hope before Axar Patel trapped the opener LBW for 21 off 16 balls.
Shimron Hetmyer and Hope added a rapid 58 runs, 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.
The hosts accelerated at the death, taking 22 runs off the 17th over to surge past the 200-run mark.
Hope smashed an unbeaten 102 off 50 balls with four fours and nine sixes, reaching the milestone with a six off the final delivery as West Indies finished on 247 for three.