The Irish looked to have shackled the Sri Lankans, as 4-15 from leg-spinner Ciara Metcalfe reduced them to 59-5 in the 10th over.
But Eshani Lokusuriyage (35 not out) and Prasdani Weerakkody (32) dragged them to 129-7.
Isobel Joyce (24) had Ireland well placed at 87-4 after 15 overs, but after she fell they slipped to 115-8.
Metcalfe said she was delighted with her own performance but disappointed by the loss.
“I am obviously happy with the way I bowled, but the defeat has hurt us,” she said. “We thought we should have won, but we will take it in our stride and continue to improve.”
Ireland are next on action on Wednesday when they take on South Africa in Chennai.
Ireland sit bottom of Group A with two defeats from two matches and will be eliminated if they lose to South Africa on Wednesday.
In Sunday’s other game, West Indies eased past Bangladesh by 49 runs.
West Indies posted 148-8 and then bowled out Bangladesh for 99 to go top of Group B, which also contains England.
Bangladesh, with three defeats from three games, go out. (Courtesy Reuters)