Pakistan, electing to bat after winning the toss, were restricted to 97-6 by the steady Bangladeshi bowling attack. Bismah Maroof top-scored with 24 and leg-spinner Rumana Ahmed claimed two wickets for 13 runs.
Bangladesh, making a strong dash for the revised Duckworth-Lewis target of 43 from seven overs following a heavy downpour during the break, scored 38-9 to lose by four runs.
Skipper Sana Mir, Sadia Yousuf and Nida Dar claimed two wickets each.
The men's competition starts on Saturday without heavyweights India and Pakistan, both of whom opted to skip the competition.