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, K.L. Rahul and Rohit Sharma shared a hundred-run opening stand before skipper Virat Kohli bludgeoned an unbeaten 70 off just 29 balls as India put on a batting masterclass to amass 240/3 in 20 overs in the series-deciding third T20I against the West Indies at the Wankhede Stadium here on Wednesday.
Openers Rahul (91 off 56b; 4x9, 6x4) and Rohit (71 off 34; 4x6, 6x5) shared a 135-run partnership to decimate the West Indies before Kohli showed why he is the best batsman in the world once again with a whirlwind 29-ball 70 (4x4, 7x6), his 100th international half-century, as the hosts set the visitors a target which, even with their firepower, would be difficult to chase.