Set 246 to win, India needed two runs off the last ball for a famous victory in the Florida sunshine.
But skipper Mahendra Singh Dhoni could only scoop a Dwayne Bravo delivery into the hands of Marlon Samuels at short third man to leave India agonisingly on 244-4.
Lokesh Rahul was unbeaten for India on 110 in just his fourth T20 match, hitting 12 fours and five sixes.