The visitors completed the second-highest successful run chase in men's T20 international history, surpassed only by South Africa's pursuit of 259 against West Indies in 2023.
Chasing a daunting target on Friday, West Indies were rocked early when paceman Mayank Yadav removed Kamil Pooran and Shimron Hetmyer with successive deliveries in the opening over and later dismissed Rovman Powell for 24.
Hope and Sherfane Rutherford turned the match on its head with a blistering 120-run partnership for the fourth wicket.
Rutherford survived on 38 when Yadav spilled a straightforward chance at short fine leg and capitalised on the reprieve, hammering 84 off 37 balls before falling to Kuldeep Yadav.
Hope remained unfazed, anchoring the chase while maintaining the required rate, and combined with Romario Shepherd to guide West Indies home with nine balls to spare. Hope was unbeaten on 102 from 45 deliveries.
Earlier, Samson's 41-ball 82 underpinned India's total after he and Abhishek Sharma raced to 42 in less than four overs for the opening wicket.
Chase halted the early surge by dismissing Sharma and later removed Kishan for 43 and Shivam Dube, while Shamar Springer struck with the key wicket of Samson.
India accelerated again at the death through Shreyas Iyer and Tilak Varma, who put on 83 runs from 32 balls, with Iyer making 40 before falling off the penultimate delivery as the hosts finished on 5-249.
The teams meet again in the third T20 in Indore on Sunday.
