They surpassed the previous record of 263-5, set by Royal Challengers Bangalore in 2013
Half-centuries by openers Tamim Iqbal and Liton Das and allrounder Shakib Al Hasan at Dublin on Wednesday helped the middle-order secure the comfortable victory.
Mushfiqur Rahim made a quickfire 35 off 33 while Mahmudullah was unbeaten at 35 off 29 after Shakib retired hurt with a side strain.
Medium pacer Abu Jayed took five wickets, but gave away 58 runs off his nine overs.
Mohammad Saifuddin took two wickets and finally the hosts were able to post a total of 292.
Starting the chase, Bangladesh were 117 for one when Tamim was out after his 45th half-century.
Now Mashrafe Bin Mortaza’s team will face West Indies in the final of the crucial pre-World Cup series on Friday.