After the early loss of John Campbell in the fifth over as they chased India's formidable 7-351 on Saturday, Hope combined with Amir Jangoo (67) for a crucial 109-run second-wicket stand to steady the innings and help West Indies reach 1-78 at the end of the powerplay.
Jangoo struck his third ODI half-century before being run out, while Sherfane Rutherford fell soon after for 24.
But Hope maintained the momentum, adding another vital 56-run partnership to keep the chase on track, and despite the dismissals of Keemo Paul and Matthew Forde, he remained in control and guided West Indies sealed victory with 10 balls to spare.
India had earlier been forced to rebuild after slipping to 2-4, but Rohit Sharma and Ruturaj Gaikwad steadied the innings with a 137-run partnership.
Sharma anchored the recovery with a fluent 92 off 85 balls before KL Rahul made the most of his lone batting opportunity of the series, bringing up his ninth ODI hundred.
Rahul accelerated sharply at the death, smashing 42 runs off the final 12 balls he faced to convert his century into a career-best ODI score.
Gaikwad chipped in with a half-century before being dismissed by Jayden Seales.
With Rahul unbeaten on 129, India finished strongly through late cameos from Naman Dhir (30 off 21 balls) and Anshul Kamboj (17 off nine balls).
Their contributions helped propel India to 351-7, with Rahul and Gurnoor Brar unbeaten at the crease.
The Shubman Gill-led side had already secured the series by winning the opening two ODIs.
In the second match, they had completed a record chase of 406 with 6.3 overs to spare to seal the series.
