Mahela Jayawardene scored 78 and Irfan Pathan took four wickets as Sri Lanka were bowled out for 254.
Earlier India set Sri Lanka a target of 305 to clinch their first one day international (ODI) cricket match of Asia Cup.
Virat Kohli top-scored for India with 108 as the India made 304-3 after losing the toss. Farveez Maharoof with 2-57 was Sri Lanka's most impressive bowler.