After winning the toss and batting first, Sobhana Mostary top-scored with 36 for Bangladesh in a below-par total of 119-7.
Their bowlers then strangled the Scotland reply and in spite of Sarah Bryce's 49 not out from 52 balls, the newcomers could only muster 103-7 in reply, handing Bangladesh their first win in a T20 World Cup in a decade.
"We have been waiting for this moment for a long time," said Bangladesh captain Nigar Sultana Joty.
"We had in our minds that this is our moment. Means a lot."
Ritu Moni was named player of the match for her parsimonious spell of 2-15 from four overs.
It was a tough opener for both sides with temperatures hitting 38 degrees celsius and the batters stymied by a sluggish pitch and slow outfield.
There were just 15 fours in the match and no sixes to cheer the sparsely-populated stands.
"It was not very easy to bat on initially," said Joty who was playing her 100th T20I.
"We had a good total and we kept believing in ourselves. We have a very good spin attack.
"We are trying to get the momentum and we got it.
"Very happy that we fought back and seeing them (the girls) smile is the biggest inspiration."
Scotland, meanwhile, were left to rue some poor fielding which saw three simple catches go to ground.
"We were a little bit sloppy in the field," said skipper Katheryn Bryce.
"A couple of misfields and overthrows. Those little things can cost you in the end.
"It was always going to be tough (playing our first match), getting over the nerves. It was nice to get out there, put in some fight."
