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India spinner Ravindra Jadeja had ripped the heart out of the innings by dismissing Johnson Charles for 60, Marlon Samuels and Ramnaresh Sarwan in the space of 14 balls but Sammy's late cameo gave West Indies hope.
Both sides won their opening matches in the tournament and a second victory would mean almost certain qualification for the semi-finals.
India captain Mahendra Singh Dhoni won the toss and put West Indies into bat in overcast conditions.
Chris Gayle struck four powerful boundaries but the West Indies dangerman was out for 21, well caught at first slip by Ravichandran Ashwin off pace bowler Bhuvaneshwar Kumar.
Charles seized the initiative, however, and dominated a second-wicket partnership of 78 with Darren Bravo.
Charles hit eight fours and two towering sixes, reaching his fifty from 46 balls before being deceived by Jadeja and trapped lbw.
The left-arm spinner then removed Samuels lbw and had Sarwan caught by wicketkeeper Dhoni down the leg side.
Bravo and his half brother Dwayne tried to repair the damage but the former, having set himself to bat through the innings, rashly charged down the wicket to Ashwin and was easily stumped by Dhoni for 35.
Kieron Pollard struck successive sixes off Ashwin but Dwayne Bravo was out for 25 and the Indian fast bowlers turned the screw in the closing overs.
They looked likely to keep West Indies below 200 until Sammy launched his withering assault, hitting four sixes and five fours mainly straight down the ground.
Sammy faced just 35 balls and shared an unbroken ninth-wicket partnership of 51 with Kemar Roach who did not contribute a single run.
Jadeja also claimed the wickets of Sunil Narine and Ravi Rampaul on the way to figures of five for 36, his first five-wicket haul in one-day internationals.
