
The hosts had already been assured of a spot in the semifinals after Sri Lanka beat Malaysia in the other Group A match at the Bangabandhu National Stadium on Friday.
Bangladesh and Nepal both progressed to the knockout stage with five points each but Maruful Haque's men went ahead on goal difference.
The hosts, who were without their best striker Jahid Hasan Amelie and midfielder Zahid Hossain, played an attacking brand of football from the start.
Shakhawat Hossain Rony and Hemanta Vincent Biswas squandered a number of straightforward chances in either half.
Rony missed a golden chance early on when he drove a shot straight at the Nepal goalkeeper from close.
Nepal slowed things down after the break and looked to counterattack, but they ended up wasting several opportunities too.
Bangladesh regained possession after Hemanta was replaced with Jewel Rana but they continued to lose the plot in the final third.
They came close again in the 83rd minute when Rony latched on to Monayem Raju's ball at the edge of the box, but he fired it inches over the bar.
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