Perera, who passed a late fitness test to be included for the game, hit 77 off 53 balls as Sri Lanka reached 158-4 in 18.5 overs after restricting Bangladesh to 155-6.
Sri Lanka never lost their grip on the match after Perera and captain Upul Tharanga put on 65 runs in the opening stand, though a double strike by Bangladesh captain Mashrafe Mortaza slowed their progress.
Mashrafe, who announced his retirement from Twenty20 International cricket before the game, removed Tharanga for 24 and took a catch off his own bowling to dismiss Dilshan Munaweera for eight.
"I tried to finish the game. (I) had a couple of injuries but recovered well," said Kusal Perera. "Every player has a couple of bad patches, (you) have to get over it, do the hard work and get out of bad patches."
Mashrafe finished with 2-32 but other Bangladeshi bowlers struggled as Sri Lanka took a 1-0 lead in the series.
Mahmudullah made 31 off 26 balls while Soumya chipped in with 29 in Bangladesh's stop-start innings at R Premadasa Stadium.
Mashrafe won the toss and opted to bat first but Bangladesh were rocked by Lasith Malinga's second ball strike.
Making a comeback in international cricket after weeks of injury lay-off, Malinga bowled opener Tamim Iqbal for a duck, though Sri Lanka could not capitalise on the wicket of the visitors' batting mainstay .
Soumya left in the same over before quick dismissals of Mushfiqur Rahim (11) and Shakib Al Hasan (11) threatened to derail Bangladesh completely.
"The way we batted in the first six overs was brilliant, but we lost too many wickets in the middle... We need to be more calculating while batting," Mashrafe said after the match.
Malinga finished with 2-38.
Tharanga praised Malinga for his efforts.
The second and final match of the series will be held at the same ground on April 6.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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