Choosing to bat, Sri Lanka posted 128/8 with opener Chamari Atapattu top-scoring with 43. Even as they lost wickets at regular intervals, Eshani Lokusuriyage lent stability to the side.
In reply, India managed only 106/9. Captain Mithali Raj fell for 16 in the eighth over and with her went India's hopes of winning. Shikha Pandey top-scored for India with 22.
In another Group B match earlier in the day, West Indies edged past England by nine runs.
Brief scores (Group B):
Sri Lanka women 128/8 in 20 overs (C Atapattu 43, L Kaushalya 34; P Yadav 2/20) bt India women 106/9 in 20 overs (S Pandey 22; K Prabodhani 2/9, H Samuddika 2/20, I Ranaweera 2/18)
West Indies women 133/7 in 20 overs (K Knight 43, S Taylor 56; A Shrubsole 2/25, N Sciver 3/18) bt England women 124/9 in 20 overs (C Edwards 44; D Dottin 4/12)
Playing today (Group A):
Ireland vs New Zealand, 3pm
Australia vs South Africa, 7pm, both in Sylhet