Chasing 125 Bangladesh achieved the target when Mahmudullah took a single off Dasun Shanaka but the overthrow ensured another run finishing the match in 19 overs.
However, Bangladesh did not get an ideal start as Dhananjaya de Silva removed Soumya Sarkar on the third ball of the iinnings.
Meanwhile, Nuwan Thushara took two wickets to further dent Bangladesh’s pursuit, reducing them to 28-3 in 5.2 overs.
Towhid Hridoy then joined Litton Das and notched a 20-ball 40 during the partnership of 63 runs to push the team’s total to 91.
Hridoy smashed four sixes during his knock including three consecutive sixes in the 11th over to Sri Lanka captain Wanindu Hasaranga before falling on the fourth ball of the over.
Hasaranga struck again in the next over dismissing Das who was playing at 36 off 38.
Mahmudullah held on to one end while wickets kept falling on the other end as Thushara picked two consecutive wickets in the 18th over.
However, Mahmudullah hit the remaining 11 runs in the 19th over off Shanaka to finish the game. The right-handed batter scored an unbeaten 16 off 13.
For Sri Lanka, Thushara led the bowling with the figures of 4-18 while Hasaranga picked two wickets.
Bangladesh invited Sri Lanka to bat and picked two wickets in the powerplay, however, Pathum Nissanka remained firm on his end.
Nissanka scored 47 runs during his 28-ball stay with the help of seven boundaries and one six before Mustafizur Rahman dismissed him to reduce Sri Lanka to 70-3.
Bangladesh took control and made it difficult for Sri Lankan batters to score runs as Dhananjaya de Silva and Charith Asalanka managed 30 runs from 32 balls for the fourth wicket.
Young legspinner Rishad Hossain dismissed Asalanka (19) and incoming batter Wanindu Hasaranga on back-to-back balls to break Sri Lanka’s momentum.
Dhananjaya de Silva (21) also fell prey to Hossain in the next over leaving Sri Lanka reeling at 109-6.
Angelo Mathews added a valuable 16 runs from 19 balls to push Sri Lanka’s total to 124-9 in their allocated 20 overs.
Bangladesh’s Rishad Hossain and Mustafizur Rahman picked three wickets each. Taskin Ahmed contributed with two wickets.