The 24-year-old batsman, leading in the absence of the injured Mahendra Singh Dhoni, smashed 13 fours and two sixes for his 14th one-day ton that helped guide the visitors to 311-7 off 50 overs.
Openers Shikhar Dhawan, with 69 off 76 deliveries, and Rohit Sharma, who contributed 46 off 78 balls, set the early platform in an opening stand of 123.
West Indies' reply never got the necessary momentum and the team was bowled out for 171 off 34 overs to lose by 102 runs on the Duckworth/Lewis method.
Seamers Bhuvneshwar Kumar (3-29), Umesh Yadav (3-32) and Ishant Sharma (2-30) led the way for India.
The hosts had been stuttering at 56-2 off 10 overs when a rain shower caused a delay of an hour and a half and resulted in a reduced target of 274 off 39 overs.
The victory was set up by India's huge total after they were sent in front of a crowd of close to 15,000.