Electing to bat, India posted a lowly 107 for eight in their stipulated 20 overs before returning to restrict West Indies to 105 for seven.
Chasing 108 to win, West Indies were comfortably placed at 57 for one in 13 overs when Deepti Sharma struck, cleaning up opener Lee-Ann Kirby (42) to trigger a collapse.
Soon skipper Stafanie Taylor (16), Chedean Nation (0) and Deandra Dottin (1) were back in the hut as West Indies slipped to 67 for five in the 17th over.
Hayley Matthews (25) and Chinelle Henry (17) blasted three fours and a six in the 19th over to leave them with 11 to get off the last six balls.
Henry blasted Poonam for a four but the Indian dismissed Matthews in the fourth ball.
West Indies needed three runs off the last ball but Henry was caught by Veda Krishnamurthy.
Earlier, India’s top-three failed to fire as they were reduced to 17 for three in 3.1 overs.
Opener Smriti Mandhana (4) lasted just six balls, while Jemimah Rodrigues (0) failed to open her account. Young Shafali Verma blasted a couple of fours before being caught by Britney Cooper off Shamilia Connell (2/20).
Skipper Harmanpreet Kaur (11), too, didn’t stay long, while Krishnamurthy was cleaned up by Afy Fletcher (1/26), as India slumped to 52 for five in 11.2 overs.
Deepti Sharma made a 32-ball 21 before becoming a victim of Anisa Mohammed (2/16), while Pooja Vastrakar (13) was removed by Aaliyah Alleyne (1/9). Stafanie taylor then got rid of Taniya Bhatia for 10.
Shikha Pandey finally smashed a 16-ball 24 to give some respectability to the total.
India women: 107 for 8 in 20 overs (Shikha Pandey 24; A Mohammed 2/16) West Indies women: 105 for 7 in 20 overs (Lee-Ann Kirby 42; Poonam Yadav 3/20).