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Chasing a modest target of 195, Hirun Matheesha anchored the innings with an unbeaten 80 off 136 balls, while Arosha Sithumina chipped in with a well-paced 50 off 63 deliveries. The visitors reached the target comfortably, finishing on 195 for four in 45.5 overs to level the series 1-1.
For Sri Lanka, Minuga Nethsara and Himaru Deshan starred with the ball, claiming three wickets each.
Bangladesh had won the series opener by 78 runs at the same venue on Sunday. The series-deciding third and final match will also be played at the same ground on Friday.