India skipper Virat Kohli, who won the toss and chose to bat, reached the 10,000-run mark in the 50-over format in style with 157 not out from 129 balls.
India hit 321-6 and West Indies, in reply, reached 321-7 with Hope scoring an undefeated 123 from 134 deliveries.
Kohli, who scored 140 in India's series-opening eight-wicket victory at the weekend, started the game on 9,919 runs from 204 innings. He struck 13 fours and four sixes on Wednesday.
Kohli and Ambati Rayudu took India from 40-2 in the ninth over to 179-3 in the 33rd with Rayudu scoring 73 off 80 before being bowled by Ashley Nurse (2-46).
Kohli also played his part in the field, catching Shimron Hetmyer for 94 off Yuzvendra Chahal.
Kuldeep Yadav was India's most successful bowler with 3-67 off 10 overs.
West Indies went into the last over — bowled by Umesh Yadav — needing 14 to win.
Both teams had made one change, with India bringing in Kuldeep Yadav to add an extra spin option at the expense of Khaleel Ahmed, and left-arm paceman Obed McCoy getting a debut for the West Indies in favor of Oshane Thomas.
The third match of the five-game series is on Saturday at Pune.