Rovman Powell's late heroics were not enough to rescue the West Indies as India held their nerve to seal an eight-run victory in the second Twenty20 in Kolkata on Friday.
The win gives the hosts an unassailable 2-0 lead in the three-match series.
With 23 needed off the last four balls, Powell (68 not out) smashed two consecutive sixes off Harshal Patel (0-46), but the seamer bowled a terrific penultimate ball to clinch the win for India, who had to contend with heavy dew in the outfield.
After struggling to 59 for 2 off 8.3 overs, the West Indies were dragged back into the match by Powell and Nicholas Pooran (62), who shared a 100-run stand that was brought to an end at a crucial moment by Bhuvneshwar Kumar (1-29) in the 19th over.
"Always a fear when you are playing against these guys," said India captain Rohit Sharma.
"We knew it would be a little tough. We were very well prepared. Under pressure, we executed all our plans. It was very critical given the point of time."
West Indies skipper Kieron Pollard added: "Powell was phenomenal today. His partnership with Pooran almost got us over the line. We did well to take it as deep as we can. We can look at different ways as to how we could have gotten those 8 runs."
Earlier, half-centuries from Virat Kohli (52) and Rishabh Pant (52 not out) had fired India to a formidable 186-5 in 20 overs.
Put into bat by the visitors, India lost openers Ishan Kishan (2) and Rohit (19) cheaply before Kohli found some form, striking seven fours and a six for his 30th career T20 fifty.
Roston Chase (3-25) struck twice in the middle overs to stem the flow of runs, but a late assault from Pant and Venkatesh Iyer (33) pushed India past 180 on a flat batting wicket at the Eden Gardens.
"It was a very important innings from Virat. He took the pressure off me. Great finish from Pant and Iyer as well. Very happy to see how he has progressed. To see such maturity is very pleasing - he backs his skills and that is what every captain wants," said Rohit.
The final match of the series will be played at the same venue on Sunday.