Mushfoqur and Mominul added 203* runs for the fourth wicket.
Bangladesh are consolidating a lead against Zimbabwe in the one-off Test in Mirpur.
They are already 86 runs ahead of the visitors with seven wickets in hand.
The hosts started the day on 240/3.
The two overnight batsmen remained unbeaten throughout the first session and added 111 runs.
Skipper Mominul Haque scored his 9th Test century and veteran Mushfiqur Rahim was not out at 99.
Mushfiqur completed his 7th Test ton just after the lunch break.
Zimbabwe were bowled out for 265 in their first innings.