Pakistan, electing to bat after winning the toss, were restricted to 97-6 by the Bangladeshi bowling attack.
Pakistani player, 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.
In the bronze medal play-off, Sri Lanka surpassed China’s modest 65-6 for the loss of five wickets in 17.1 overs.
The men’s competition starts on Saturday without heavyweights India and Pakistan, both of whom opted to skip the competition.