Chasing a daunting target, 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.
"But when you chase here in India, you always give yourself a chance. You always think you're in the game, regardless of what score is on the board," Hope said.
"But five for two was always going to be challenging."
Skipper 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 spilt 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 remained unbeaten on 102 from 45 deliveries.
"When we got that partnership there, we just got some more impetus in the innings," Hope said.
"Then obviously Sherfane came and did what he did, played really well with the bat, and just gave us that spark that we needed to get over the line today."
This is 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.
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 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 249-5.
The teams meet again in the third T20 in Indore on Sunday.