Sri Lanka triumph in rain-affected first ODI against West Indies
Chasing a revised target of 232 in 37 overs, the hosts raced to victory with 5.3 overs to spare.
After a shaky start that saw Sri Lanka slump to 45 for three in the seventh over, Asalanka's arrival at the crease turned the tide.
His partnership with Madushka, worth 137 runs for the fourth wicket, came in rapid time.
Both Asalanka and Madushka reached their half-centuries in just 44 balls.
Madushka, who has played 10 Test matches, was brought in to replace injured opener Pathum Nissanka, the leading run scorer in ODIs in 2024.
"I am glad that he has grabbed the opportunity with both hands," Asalanka said. "It is good to have healthy competition in the side."
The West Indies had posted 183 for four in 38.3 overs before rain intervened.
Their spinners then found it hard to grip the wet ball.
"We were really tested by the conditions", West Indies skipper Shai Hope said.
"Particularly for the spinners, the wet ball was quite challenging."
Gudakesh Motie eventually broke the Asalanka-Madushka stand, when Brandon King took a sharp catch at slip.
But by then, the damage had been done.
Sri Lanka needed just 50 runs off 74 balls when Madushka fell for 69 off 54 balls, which included seven fours and a six.
Motie also trapped Asalanka lbw after a brilliant 77 off 71 balls, studded with eight fours and three sixes.
Motie finished with three wickets, although he could have had a greater impact if not for the challenging conditions, with the ball having to be changed twice.
Kamindu Mendis and Janith Liyanage saw Sri Lanka home comfortably.
Earlier, the West Indies had struggled against Sri Lanka's spinners, but Sherfane Rutherford's career-best 74 not out, combined with support from Roston Chase, helped the visitors recover with an unbroken 85-run partnership for the fifth wicket.
However, it was not enough to stop Sri Lanka from taking the lead in the series 1-0.
Sri Lanka came from behind to win the T20 series 2-1 last week, their first series win over the West Indies in the shortest format.
The remaining two ODIs will be held on Wednesday and Saturday.