Chasing 296, India reached 299 for two in only 41.4 overs, with Kohli completing the chase in emphatic fashion. The veteran batter struck nine sixes in his 88-ball innings, including the winning blow, while captain Shubman Gill contributed 110 from 108 deliveries.
The result gave India a 1-0 lead and added another memorable chapter to Kohli's career. During his innings, he became only the second player after Sachin Tendulkar to surpass 15,000 ODI runs.
Kohli reached the milestone in his 303rd ODI innings, considerably faster than Tendulkar, who required 377 innings to reach the mark. His century was also his 55th in ODI cricket and 86th across international cricket.
Gill, meanwhile, produced another substantial contribution at the top of the order. He brought up his 10th ODI century and shared a 151-run second-wicket partnership with Kohli, effectively ending West Indies' hopes of defending their total.
Earlier, West Indies had appeared capable of posting a much larger score after an excellent start.
Justin Greaves and John Campbell put together 135 for the opening wicket, with Campbell scoring 62 and Greaves going on to register his maiden ODI century. Greaves took advantage of India's early struggles, driving confidently against the new ball and helping West Indies maintain a strong scoring rate through the opening stages.
India eventually turned the match around through Kuldeep Yadav.
Returning to the ODI side, the left-arm wrist-spinner claimed four wickets for 40 runs and was central to a dramatic middle-order collapse. After Campbell's dismissal, West Indies slipped from 176 for one to 198 for five, losing four wickets for just 22 runs.
Kuldeep dismissed Campbell after beating him in flight, before striking again during a crucial passage in which India's bowlers restricted the scoring. Greaves eventually fell for 101, while Jewel Andrew was dismissed soon afterwards, leaving West Indies in danger of being bowled out for a modest total.
Amir Jangoo prevented that collapse from becoming decisive. His aggressive unbeaten 58 from 43 balls, supported by Roston Chase, helped West Indies recover from 198 for five and finish on 295 for seven.
That recovery proved just enough to provide India with a competitive target, but the home side's top order made the chase look considerably easier than it might have appeared.
Rohit Sharma, playing alongside Kohli in India's ODI plans ahead of the 2027 World Cup, provided a brisk start with Gill. The pair added 74 before Sharma fell for 32 in the 12th over.
Gill then continued the assault before Kohli joined him at the crease. The two batters steadily increased the tempo, combining controlled accumulation with aggressive strokeplay to take the game away from West Indies.
Gill eventually departed for 110, but by then India required only a small number of runs. Ruturaj Gaikwad's 13 was enough to support Kohli as the experienced batter completed the victory with consecutive boundaries.
The second ODI will be played in Guwahati on Wednesday, with India taking a 1-0 advantage into the next match.
Virat Kohli moved closer to Sachin Tendulkar's historic international century record on Sunday as he marked another milestone during India's eight-wicket ODI win over West Indies.
David Miller produced a career-best innings and Temba Bavuma added a century while the spinners dominated for the Proteas as they secured a second consecutive victory over Australia, winning the second ODI by 32 runs at the Wanderers in Johannesburg.
Tom Banton marked his return to England's one-day side in style, smashing his maiden international century as England thrashed Sri Lanka by 223 runs at The Oval.
Virat Kohli and Rohit Sharma are still very important voices in the India dressing room, despite now only playing one of the three formats, according to bowling coach Morne Morkel.
