The foundations to Sri Lankas highest-ever successful T20 chase were laid by the openers Mendis and Danush Gunathilaka, whose rambunctious 53-run partnership compiled in 4.5 overs made a serious dent in Bangladeshs 193/5 and enabled the middle-order to coast to victory with 3.2 overs to spare.
Mendis was adjudged the man-of-the-match for his 53 off just 27 balls, studded with eight fours and two sixes.
Sri Lanka recently won the two-match Test series 1-0 and will look to stretch their dominance into the short T20I series before heading home for the tri-nation Nidahas Trophy that marks their 70th year of independence.
The Bangladesh Cricket Board said it would consider appealing the demerit points but promised to take more precautions in future.
On the other hand, Bangladesh will be without all-rounder Shakib Al Hasan, who has picked up a finger injury. He was assisted well by former captain Mushfiqur Rahim, who top scored for his team by scoring a fluent 66 runs of 44 balls and was unbeaten till the end of the innings.
Sarkar put on stands of 49 and 51 with Zakir Hasan and Mushfiqur before an ugly reverse sweep helped Jeevan Mendis strike lbw with his first ball and left the batsman needing help from team-mates to leave the pitch. Sri Lanka's previous-best T20 chase of 176 came against Australia.
The second match of the series will be held in Sylhet on Sunday.