Dashun Shanaka, who took two wickets, gave only eight runs in the last over.
However, Angelo Mathews was the pick of the Sri Lankan bowlers. He took two wickets for 17 runs in three overs. Binura Fernando also got two apiece while Mahesh Theekshana and Mathisha Pathirana got one apiece.
Earlier in the day, Bangladesh captain Nazmul Hossain Shanto won the toss and elected to bowl first in the first T20 match.
Stand-in captain Charith Asalanka played a blistering inning of 44 runs to take Sri Lanka to a mammoth score of 206/3.
Asalanka hit six sixes in his innings of 21 balls. He got wonderful support at the other end from Sadira Samarawickrama, who remained unbeaten on 61 off 48 balls. Sadira hit eight fours and one six.
Thanks to wicketkeeper batsman Kusal Mendis, the visiting team got a relatively good start. Despite losing his opening partner Avishka Fernando in the very first over by Shoriful Islam, the right-handed batsman did not lose his composure. He scored 59 runs in 36 balls with the help of six fours and three sixes.