The Windies lost destructive opener Evin Lewis even before they started their chase as the opener picked up a knee injury while fielding and could not continue.
The visitors were reduced to 17/3 before Kieron Pollard (68) and Shimron Hetmyer (41) shared a 74-run stand for the fourth wicket to keep the visitors in the game. But once Hetmyer hit Kuldeep Yadav straight down long on's throat where Rahul took the catch, it looked all over.
However, Pollard kept their slim chances alive with some big hitting. The captain finally got out, trying to go for one too many as the asking rate was touching 20 runs per over.
Bhuvneshwar Kumar had the West Indian caught by substitute Ravindra Jadeja at deep midwicket in the 15th over, and from there on it was only a matter of time before India wrapped up the proceedings as West Indies managed 173/8 in the end of 20 overs.
Mohammed Shami, playing his first T20I after two-and-a-half years, returned impressive figures of 2/25 from his four overs, while Kuldeep Yadav -- back in the side after a while -- Bhuvneshwar and Deepak Chahar also picked up two wickets each.
Earlier, Skipper Virat Kohli 70* (29) provided a great finishing touch following fiery knock from the opening duo of Rohit Sharma 71 (34) and Kl Rahul 91 (56) to propel team India to 240/3 in their 20 overs against West Indies at Mumbai's iconic Wankhade's stadium.
(With IANS Inputs)