The West Indies reached 352-5 in 48.2 overs, completing their highest successful run chase in ODI cricket with 10 balls to spare.
India had already secured the three-match series after winning the opening two matches, but the West Indies ended the series on a high with their first ODI victory over India since 2023.
Hope produces an extraordinary innings
Hope was the star of the chase, finishing unbeaten on 162 from 143 balls, with 17 fours and three sixes.
His innings was even more remarkable because he had kept wicket for all 50 overs of India's innings before opening the West Indies chase.
The 31-year-old also battled a groin problem towards the end of his innings but remained at the crease to hit the winning run.
His 162 was the highest individual score by a West Indies batter in a successful ODI run chase, surpassing Brian Lara's previous national record of 153 against Pakistan in 1993.
Hope also brought up his 21st ODI century, reaching three figures from 104 balls.
Jangoo provides crucial support
The West Indies lost John Campbell early, but Hope found an excellent partner in Amir Jangoo.
The pair added 109 runs for the second wicket, with Jangoo scoring 67 from 56 balls before being run out.
Sherfane Rutherford then contributed 24, while Keemo Paul struck 44 from 35 balls to keep the required rate under control.
With the West Indies needing a strong finish, Gudakesh Motie provided valuable support to Hope with an unbeaten 19 from 14 balls.
India post 351 despite early setbacks
India were put under pressure early after Jayden Seales dismissed captain Shubman Gill for one before removing Virat Kohli for a golden duck.
Rohit Sharma and Ruturaj Gaikwad then rebuilt the innings with a 137-run partnership.
Rohit made 92 from 85 balls before falling short of a century, while Gaikwad contributed 57.
KL Rahul, playing his first match of the series, then produced an unbeaten 129 from 87 balls to give India a formidable total of 351-7.
Rahul struck 16 boundaries, including six sixes.
West Indies complete historic chase
The visitors remained in control for much of their pursuit despite losing wickets in the middle and final stages.
India briefly threatened to turn the match around when Keemo Paul and Matthew Forde departed, but Hope's presence at the crease proved decisive.
He accelerated dramatically in the closing overs, reaching 150 before Gudakesh Motie helped take the pressure off his captain.
The West Indies eventually crossed the line at 352-5 in 48.2 overs to seal a five-wicket victory.
Match summary
• India: 351/7 in 50 overs — KL Rahul 129*, Rohit Sharma 92, Ruturaj Gaikwad 57
• West Indies: 352/5 in 48.2 overs — Shai Hope 162*, Amir Jangoo 67, Keemo Paul 44
• Result: West Indies won by five wickets
India win series 2-1
Despite the defeat, India won the ODI series 2-1 after their victories in the opening two matches.
India's captain Shubman Gill acknowledged that the team still needs to improve its death bowling and fielding ahead of the 2027 Cricket World Cup, pointing specifically to missed catches and uncertainty during the final overs.
The two teams will now turn their attention to a five-match T20I series, beginning in Lucknow on 6 October.