Returning to the team after being rested for the first two matches, Bumrah emerged the most effective bowler, conceding just 35 in his 10 overs.
Bumrah sent both the visiting openers -- Kieran Powell (21) and Chanderpaul Hemraj (15) -- in his first spell to give India a solid start and later dismissed Hope and Ashley Nurse (40).
Hope, who had struck an unbeaten 123 in the Visakhapatnam ODI, played a significant role in reviving the Caribbean innings with his 95-run knock, which came off 113 balls.
Towards the end, Nurse and Kemar Roach (15 not out) added crucial 56 runs for the ninth wicket, taking the side close to 300-run mark.
The West Indies batsmen got starts but could not convert them into big knocks and also struggled to form big partnerships.
Hope, though, dug in from one end, raising a 56-run stand with Shimron Hetmyer (37) for the fourth wicket. The credit to break that partnership goes to former skipper M S Dhoni's brilliant glove work as he took the bails off with lightening speed when Hetmeyer was marginally outside the crease, trying to launch Kuldeep Yadav (2/52).
Before that stumping, Dhoni had taken a breath-taking catch to remove Kieran Powell, racing towards the backward square leg boundary and diving to hold on to the top-edge off Bumrah.
It was a sort of statement by the charismatic Dhoni, who was left out of India's Twenty20 squad on Friday.
Hope also combined with skipper Jason Holder (32) for a 76-run stand for the sixth wicket.
Continuing with his good form and combative attitude, Hope handled the middle overs with elan. He was severe against Yuzvendra Chahal, whom he hit for sixes with ease never letting the bowler dominate.
However, Bumrah denied him the milestone mark by hitting the timber with a well-executed yorker. Hope's knock was studded with six fours and three sixes.
The innings looked like falling apart again but Nurse and Roach contributed 55 runs with combined eight boundaries to ensure they have a fighting total.