In the day's other match, a gritty 68 off 53 balls from opener Mohammad Shahzad and an unbeaten 51 from 24 balls from Shafiqullah helped Afghanistan to a seven-wicket win over Hong Kong to keep their hopes alive in the tournament.
The winners of qualifying groups A and B will join the eight top-ranked countries in the next stage of the March 16-April 6 tournament.
Bangladesh, who beat Afghanistan in their first match, chased down a paltry 127-run target with 27 balls to spare, powered by a 33-ball 42 from opener Anamul Haque.
Anamul, who hit five fours and two sixes, gave Bangladesh a brisk start and added 63 for the first wicket with Tamim Iqbal (30) after the bowlers restricted Nepal to 126 for five in their 20 overs.
Anamul's run-out brought all-rounder Shakib Al Hasan to the crease and he ensured the home team significantly improved their net run rate with a 18-ball 37, studded with four sixes and four.
Paceman Al-Amin Hossain led the Bangladesh bowlers with figures of two for 17 runs as Nepal, who beat Hong Kong in their opening match, struggled for momentum after being put into bat.
Earlier, Shahzad and Shafiqullah, who hit five fours and three sixes, added 47 for the third wicket to lift Afghanistan, who chased down their target of 154 with two overs to spare.
Afghan captain Mohammad Nabi, spinner Hamza Kotak and paceman Shapoor Zadran picked up two wickets each to restrict Honk Kong to 153 for eight in their 20 overs.
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- Mohammad Shahzad