Sharma scored an unbeaten 152 while Kohli made 140 to easily overhaul a challenging total of 323 runs with almost eight overs to spare. The two batsmen were involved in a 246-run partnership.
Earlier, put in to bat, the West Indies innings was anchored by a brilliant 106 by Shermon Hetmyer.
Hetmyer smashed six fours and six sixes to third century in just 13 games. Important contributions from Jason Holder, Devendra Bishoo and Kemar Roach helped the visitors post a competitive total of 322 runs in 50 overs.
In reply, India lost opener Shikhar Dhawan in just the second over. However, Kohli and Sharma took charge with the Indian captain scoring his 36th hundred in just 88 deliveries while Sharma scored his 20th ODI hundred.
“Feels pretty good. A convincing win. I thought West Indies were really good with the bat. And 320 plus totals are always tricky,” Kohli said after the win.
“But we knew it's all about one partnership. And life isn’t difficult when Rohit is at the other end. It’s our 5th or 6th double-century partnership, it's a pleasure to bat with him,” he added.