Mushfiqur was the last batter dismissed after scoring a scintillating 137 off 233 balls, an innings laced with 12 fours and one six. Liton Das, who made a sublime 126 in the first innings, followed it up with an elegant 69.
Resuming the day at 110-3, Bangladesh suffered an early setback when by Khurram Shahzad trapped skipper Najmul Hossain Shanto leg-before with a sharp inswinger in just fourth over of the morning.
However, Mushfiqur and Liton then negotiated a disciplined Pakistan attack with equal unwavering resolve to wrest control back.
The pair eventually put Bangladesh firmly on top by sharing 123 runs for the fifth wicket.