Mushfiqur remained unbeaten on 66 off 44 balls while Soumya hit a 32-ball 51 -- the left-handed openers maiden T20 fifty -- after the hosts elected to bat first.
Bangladesh surpassed their previous highest T20 score of 190-5 against Ireland at Belfast in 2012.
Sri Lankan leg-spinner Jeevan Mendis claimed two wickets.
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