India looked in complete control after Virat Kohli’s unbeaten 89 took them to 192-2 and Chris Gayle fell for five.
But Lendl Simmons, who was twice caught off no-balls and held on the boundary only for Ravindra Jadeja to step on the rope, clubbed 82 from 51 balls.
Then Andre Russell won it with a six with two balls to spare in Mumbai.
West Indies, champions in 2012, follow their women’s team into the final after they defeated New Zealand earlier on Thursday.
The meeting with 2010 winners England in Kolkata will see a two-time World T20 champion crowned for the first time, while India’s exit extends the wait for a host nation to lift the trophy. (Courtesy BBC Sport)