Samuels smashed nine sixes, four of which came off the final five balls of his side's innings, in scoring an unbeaten 85 off just 43 balls as West Indies posted 197 for four batting first in Dhaka.
Bangladesh battled hard in reply, with Tamim Iqbal and Mahmudullah both scoring unbeaten fifties, but they struggled to keep up with the required run-rate and, despite having nine wickets still in hand, finished short on 179 for one.
Seeking to avenge their surprise 3-2 loss in the ODI series, the West Indies suffered an early blow after opting to bat first when they lost the big-hitting Chris Gayle for just six.
Gayle's opening partner Dwayne Smith followed soon after for 24 as the tourists slipped to 30 for two, but the ICC World Twenty20 champions hit back in savage fashion, led by Samuels.
Making the most of being dropped twice by wicketkeeper Mushfiqur Rahim, Samuels shared in a rapid 66-run stand for the third wicket with Darren Bravo, who scored 41 off 28 deliveries, and then, after Kieron Pollard had come and gone for a quickfire 15, put on a stunning 76-run stand in just 5.2 overs with Lendl Simmons.
Simmons contributed just 18 to that partnership as Samuels tore into the Bangladesh attack, striking three fours to go with his nine sixes and hitting Rubel Hossain for 28 off the last five balls of the innings.
That late onslaught ultimately proved the difference between the sides as Bangladesh failed to really threaten their target despite unbeaten knocks from opener Tamim, who scored 88 off 61 balls, and Mahmudullah, who finished on 64 from 48 deliveries.