Defender Masura Parvin scored the winner at the Changlimithang Stadium in Thimphu on Sunday.
They could not attack from the midfield as they kept making passing errors.
Strikers Shopna and Krishna Rani Sarker could not test the Nepalese goalkeeper.
Maria Manda’s long range shot also found the gloves by the end of the first half.
A running Masura broke the deadlock with a header in the 49th minute from Mishrat Jahan Mousumi’s free kick awarded for a foul on Shopna.
Nepal, who stunned India in penalty shootouts in the semifinal, had a chance to equalise two minutes later, but they were denied by the post.
Bangladesh could not extend the lead either, but defended the slim lead in the rest of the match to erupt in ecstatic celebrations after the final whistle.
On the way to the final, Golam Rabbani Chhoton’s team started with a 17-0 rout of Pakistan and then defeated Nepal 2-1 to become the group champions.