A spectacular middle-order collapse saw Sri Lanka make just 179 from 47.
1 overs and India had few problems reaching the target in 32.2 overs, scoring 180 for three.
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Although Sri Lanka still have one game remaining in the series, against Australia on Friday, they cannot reach the finals and it has been a disappointing tournament for last year's World Cup finalists.
Importantly for India, star batsman Sachin Tendulkar burst out of his form slump ahead of the finals against Australia with his first half-century of the series.
Tendulkar was back to his brilliant best as he punished the bowlers, hitting three successive boundaries off seamer Ishara Amerasinghe in making 63 from 54 balls, including 10 fours.
Gautam Gambhir continued his impressive form with an unbeaten 63, while Yuvraj Singh looked dangerous with a rapid 36.
Sri Lanka had appeared to be cruising towards a big total at 72 for one after being sent in to bat, with veteran opener Sanath Jayasuriya back in some touch and Ku