Bangladesh skipper Litton Das lost the toss and the Tigers were asked to bat first in the first T20I of the three-match series in Kandy on Thursday.
After finishing ninth in the 2023 World Cup and missing out on a Champions Trophy berth, the islanders have staged a commendable turnaround, notching up series wins against heavyweights India and Australia.
Asalanka smashed a career-best 127 before chipping in with the crucial wicket of Alex Carey, while Maheesh Theekshana took 4-40 to help scuttle Australia's chase.
Sri Lanka named a 16-member squad on Monday, led by Charith Asalanka for the two-match ODI series against the touring Australian team.
A captain's knock by Charith Asalanka steered Sri Lanka to a hard-fought four-wicket victory over New Zealand with six balls to spare in Saturday's Twenty20 opener in Dambulla.
Sri Lanka named their squads Wednesday for two T20s and three ODIs at home to New Zealand, with Charith Asalanka captain in both formats.
In a game that swung back and forth, India seemed to be heading towards a win after Shivam Dube smashed Wanindu Hasaranga for a six in the 47th over followed by a four in the next over by Charith Asalanka.
Sri Lanka have announced the squad for the three-match ODI series against India, starting on August 2 in Colombo with Charith Asalanka leading the side.
The 27-year-old replaces Wanindu Hasaranga, who stepped down as skipper in the shortest format after Sri Lanka failed to make the Super Eight stage of the T20 World Cup in the U.S. and West Indies last month.
Bangladesh need 207 runs to win
The vice-captain's third ODI hundred, with nine boundaries, helped the hosts keep a formidable total after several batters threw away their wickets early.
Spinners Dunith Wellalage and Charith Asalanka bagged nine wickets between them as Sri Lanka bowled out India for 213 in a Super Four clash of the Asia Cup on Tuesday.