Asked to chase 322 for victory at the ACA-VDCA Cricket Stadium, West Indies just came up short after requiring 14 from the final over.
The visitors needed five from the last ball for victory and the right-handed Hope sliced speedster Umesh Yadav to the point boundary to ensure the scores finished level.
Hope ended unbeaten on 123 from 134 balls with 10 fours and three sixes while 21-year-old left-hander Shimron Hetmyer narrowly missed out on his second straight century when he was dismissed for 94.
Left-arm spinner Kuldeep Yadav was the best bowler with three for 67.
Earlier, India captain Virat Kohli struck a magnificent unbeaten 157 as India piled 321 for six off their 50 overs, after opting to bat first.