Chasing a paltry 96-run total, opener Rohit Sharma led the Indian chase with 24 runs. Earlier, debutant fast bowler Navdeep Saini bowled brilliantly to claim three wickets as India restricted a reckless West Indies to a paltry 95 for nine in 20 overs.
While Saini made a sensational debut, scalping three wickets for 17, seasoned pacer Bhuvneshwar Kumar claimed two big wickets in India's triumph. Washington Sundar, Khaleel Ahmed, Krunal Pandya and Ravindra Jadeja had one wicket each to their name.
The Indians were also helped by the reckless approach of West Indian batsmen.
Chasing a below par 96-run target for a win, India had quite the few hiccups before reaching the target with 2.4 overs to spare. None of the batsmen contributed big with opener Rohit Sharma top-scoring with 24 while captain Virat Kohli and Manish Pandey making 19 each.
India struggled in their run chase and they were reduced to 32 for 2 in the seventh over with opener Shikhar Dhawan (1) and wicketkeeper Rishabh Pant (0) dismissed cheaply.
Rohit's 24 came from 25 deliveries with the help of two fours and two sixes on a pitch which was not easy to bat on.
Veteran off-spinner Sunil Narine (2/14) did not allow India to get off to a good start by removing Rohit and Pant in consecutive deliveries in the seventh over.