Kohli top scored with 86 while Rohit made 72. They had a 133-run partnership for the second wicket. India chased 212 in 35.2 overs.
Earlier, Indian spinners Ravindra Jadeja and Suresh Raina exploited the conditions effectively and shared six wickets between them to bundle out the West Indies for a meagre 211.
While Jadeja finished with three for 34, Raina took three for 37. R Ashwin also chipped in with two for 42 at the Nehru stadium.
Darren Bravo was the lone West Indian batsman to cross the 50-run mark, hitting a patient 77-ball 59, laced with four fours and two sixes.
Opting to bat, West Indies lost Chris Gayle off the very first ball of the match as the destructive batsman fell short of his ground while trying to take a risky single.
Here are the pictures.
Suresh Raina took 3/34, his best ODI bowling. Here, he is seen celebrating the wicket of Lendl Simmons (not pictured). Also seen is Darren Bravo.
Ravindra Jadeja takes a superb catch off his own bowling to dismiss Charles.
Chris Gayle in pain
Opener Chris Gayle grimaces in pain as he lies on the ground. He was run out for a duck.
Gayle carried off the ground
Gayle is carried off the ground on a stretcher.
End of a fine innings
Darren Bravo is bowled by Mohammed Shami. He was the top scorer for the visitors with 59.
Bhuvneshwar on target
Bhuvneshwar Kumar is congratulated by his team-mates after his direct hit got Gayle run out.
Shami (second left) celebrates with his team-mates after dismissing Darren Bravo.
Jadeja is all smiles after taking another wicket.
Raina collides with Darren Bravo.
Virat Kohli and Rohit Sharma run between the wickets during their 133-run partnership for the second wicket.
5,000 ODI runs for Kohli
Kohli completed 5,000 ODI runs today. He has equalled Vivian Richards record of being the fastest to the milestone, in 114 innings. He made 86 today.
Kohli in action
Kohli plays a shot en route to his 86.
A wicket for West Indies
West Indies players celebrate a wicket.