West Indies captain Shai Hope won the toss and elected to bat first, with his team scoring 4-185 in 38.3 of their 50 allotted overs before rain halted the game at Pallekele.
When play resumed, Sri Lanka were given a target of 232 in 37 overs under the DLS method and reached their target on 5-234 with 31 deliveries to spare.
Sri Lanka lost their first wicket with the score on six when Avishka Fernando (5) was out caught at covers by Roston Chase off fast bowler Alzarri Joseph (2-39 in six overs).
Kusal Mendis (13) skyed one off Joseph and wicketkeeper Hope took a good high catch.
Sri Lanka were three down for 45 when Sadeera Samarawickrama (18) was bowled by left-arm spinner Gudakesh Motie with a flighted, turning delivery.
Asalanka and Madushka then came together for their 109-ball partnership.
Asalanka top scored with 77 off 71 deliveries including three sixes and eight boundaries. Madushka, standing in for injured regular opener Pathum Nissanka, hit a six and seven boundaries in his 69 off 54 deliveries.
West Indies spinners struggled to grip the ball after the rain and, to make matters worse, their seamers erred in their accuracy.
Motie (3-47 off eight overs) had both Madushka and Samarawickrama out later but it was too late.
Earlier, Sherfane Rutherford and Chase added 85 in an unbroken fifth-wicket stand to give West Indies a competitive score before the rain intervened.
Rutherford was 74 not out off 82 deliveries including three sixes and five boundaries. Chase was a run-a-ball 33 not out.
Leg spin bowler Wanindu Hasaranga took 2-18 in six overs for Sri Lanka.
The one-day international series continues on Wednesday at the same venue with the second of the three games.
