Chasing 140 for victory, Bangladesh reached 141 for 4 in 19.1 overs, thanks to a blazing half-century from Juairiya Ferdous and a composed unbeaten partnership between Sharmin Akhter and Shorna Akter.
After the bowlers restricted the Netherlands to 139 for 8, Bangladesh made a confident start to the chase.
Juairiya took the attack to the Dutch bowlers, smashing 50 off just 33 balls with seven fours and two sixes. She shared a 67-run opening stand with Dilara Akter, who contributed 26.
The chase briefly lost momentum when Bangladesh lost Juairiya, captain Nigar Sultana and Sobhana Mostary in quick succession, slipping to 85 for 4 in the 12th over.
However, Sharmin Akhter and Shorna Akter ensured there would be no further setbacks. The pair added an unbeaten 56-run stand for the fifth wicket, calmly guiding Bangladesh over the line. Sharmin remained unbeaten on 37 from 32 balls, while Shorna finished on 18 not out.
Earlier, Netherlands captain Babette de Leede top-scored with 50 off 45 deliveries to help her side post a competitive total after being asked to bat.
Bangladesh's bowling effort was led by Marufa Akter, who claimed 2 for 31, while Fariha Trisna, Rabeya Khan, Ritu Moni and Sanjida Akter Meghla picked up a wicket each.
The victory not only kept Bangladesh firmly in contention in Group 1 but also marked their highest-ever successful chase in Women's T20 World Cup history.