West Indies posted 247-3 in Hyderabad, powered by skipper Hope's blistering 50-ball knock and his unbroken 91-run stand with Sherfane Rutherford, who finished on 49 not out.
Keemo Paul then led the bowling charge with figures of 5-41 to bowl out India for 223 as West Indies bounced back to level the five-match series at 2-2, setting up a decider on Sunday in Bengaluru.
Hope struck his third T20 international hundred -- the most by any West Indian batter -- and his second of the series.
West Indies started briskly before they lost Jewel Andrew for 21, but Shimron Hetmyer, who hit 33 off 12 balls, gave Hope company in another quick partnership.
Pace bowler Prince Yadav had Hetmyer caught and bowled but West Indies were never short of power as Rovman Powell contributed 24 off 17 balls.
Hope kept up the onslaught in tandem with Rutherford and brought up his century with the final ball of the innings after hitting Nitish Kumar Reddy for successive sixes.
In reply, Sanju Samson got India off to a strong start with his 23-ball 56 but the West Indies bowlers struck regular blows to keep India in check.
Medium-pace bowler Paul struck twice in the fifth over to dismiss Samson and then Ishan Kishan in the space of four balls.
Skipper Shreyas Iyer struggled for momentum before he fell to Shamar Springer for 16.
Left-arm spinner Gudakesh Motie also took wickets in one over, removing opener Abhishek Sharma for 29 before Naman Dhir was stumped for a first-ball duck.
With India needing around 14 per over to win the game, Tilak Varma, who hit 43, and Reddy (41) attempted to pull things back in their quickfire partnership worth 70.
Romario Shepherd had Varma caught and then Paul struck thrice in an over, including the wicket of Reddy, to claim his second five-wicket T20 haul and shut down India's chase.
Number 10 Arshdeep Singh retired hurt after getting hit on his shoulder by a Shamar Joseph bouncer and India's innings folded in 19.3 overs.
