Kohli upped the ante in the tail end of India's innings to finish an unbeaten 157 from 129 balls as India finished at a formidable 321/6.
Needing five runs on the final ball to chase down West Indies´ target of 322, Hope - who made a total of 123 - got four off Indian paceman Umesh Yadav as the tourists ended on 321-7 in their 50 overs.
India would look to extend their lead while West Indies aim for a leveller as they face each other in the second One-day worldwide at the Dr Y S Rajasekhara Reddy ACAVDCA Cricket Stadium on Wednesday.
Kohli needed only another 22 balls to reach 150 as India plundered 100 runs off the last 10 overs.
There were 164 ODIs with two centuries, 10 half-centuries and a batting average of 25.36 while, with the ball, he took 199 scalps at an average of 29.51.
In the first match against the Caribbean side, Kohli notched up his 36th ODI hundred as he stroked his way to a breezy 140, helping the home team take a 1-0 lead in the five-match series.
He put on 139 runs for third wicket with Ambati Rayudu, who made 73.
Kohli has been close to unstoppable in 2018, across formats. Rayudu was bowled by spinner Ashley Nurse.
A six down the ground off debutant left-arm pacer Obed McCoy brought up 1,000 runs for him in the year.
Besides Tendulkar and Kohli, Sourav Ganguly, Mahendra Singh Dhoni and Rahul Dravid are the other Indian cricketers to cross 10000 runs in the format. "However, I must accept that for me to preserve my longevity as a professional cricketer, I must do as others before have done, leave the global arena for the next generation of players", he said.
A 143-run partnership ensued between Hetmyer and Shai Hope for the fourth wicket as the duo took calculated risks. "Attractive partnership between both those guys but the way two teams played it was a fair result", Indian captain Virat Kohli said after the match.
Kohli will be playing the full ODI series after having played two Test matches as per the 15-member squad announced by the BCCI on Thursday.
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