Ali Ashfaq, named man of the match, added another in the 74th minute from a penalty (2-0).
The Maldives won the spot-kick as Bangladesh’s Sohel Rana made a rash tackle inside the danger zone.
The archipelagic state wrapped up the win they deserved after dominating the match against the men in red and green.
Five Bangladeshi booters – Md Ibrahim, Yeasin Arafat, Jewel Rana, Tariq Kazi and Jamal Bhuyan – were cautioned with yellow cards. However, goalkeeper Anisur Rahman Zico pulled up some brilliant saves.
Bangladesh last beat the Maldives in SAFF Championship in Dhaka in 2003.
Despite Thursday’s defeat, the men in red and green remained in second place of the standings with four points from three matches after beating Sri Lanka 1-0 and playing out to a 1-1 draw with India.
So far, Nepal have dominated the competition with an unbeaten run, securing six points from two matches. Bangladesh will face the Himalayan nation on 13 October at 5:00pm at the same venue.