Afif Hossain top-scored with 38 off 27 balls for Bangladesh, who posted 144-8, before Taskin took out Vikramjit Singh and Bas de Leede with the first two balls of the Dutch reply.
Two run-outs left the Netherlands on 15-4 although Colin Ackermann's 62 off 48 balls ensured they did not totally collapse before he became Taskin's fourth victim after being caught on the fence.
Number 11 batter Paul van Meekeren had an entertaining cameo of 24 off 14 balls - one of only three Netherlands batters to get to double figures - to give the first-round qualifiers a flicker of hope.
But with 12 needed from the last two balls, he was unable to clear the rope off Soumya Sarkar, who claimed the final wicket when Van Meekeren slogged to Litton Das at deep midwicket as the Netherlands were all out for 135.
Bangladesh next take on South Africa in Sydney on Thursday while Netherlands will look to put up a better showing against India in their next match.