Ireland were set a revised target of 104 runs in eight overs after Bangladesh posted a huge 207/5 in 19.2 overs as rain came to play a spoilsport and halted the proceedings for more than an hour.
Ireland got off to a blistering start by scoring 18 runs in the first over but finished on 81/5 in 8 overs.
Taskin forced the visitors to slow down with his three-wicket burst in the fourth over before claiming another wicket in the final over to finish with 4-16, his career-best figures in T20Is.
Gareth Delany top-scored for Ireland and was unbeaten on 21.
Earlier Rony Talukdar struck a career-best 67 from 38 balls to power Bangladesh after stand-in Ireland skipper Paul Stirling won the toss and elected to bowl.
Rony put on 91 runs in just seven overs in an opening stand with Liton Das, who made 47 off 23 balls.
Craig Young broke the stand when he forced Liton to hole out to Stirling at mid-off and Harry Tector soon had Najmul Hossain stumped for 14.
Ireland were hoping to put the brakes on Bangladesh’s scoring spree once Graham Hume bowled Rony, who smacked seven fours and three sixes in his maiden T20I fifty.
However, Shamim Hossain’s 20-ball 30 and Shakib Al Hasan’s 20 not out off 13 balls helped Bangladesh race past the 200-run mark before rain brought a premature end.
Right-arm pacer Young claimed 2-45 for Ireland.
The game was Bangladesh’s first T20I at home against Ireland, who have rested regular skipper Andrew Balbirnie for the three-match series.
The second match is scheduled at the same ground on Wednesday.
Bangladesh won the preceding three-match one-day international series 2-0. The teams will meet for a one-off Test in early April.
(With AFP Inputs)
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