The hosts were 303 for five at stumps.
Mushfiq remained unbeaten with 111 runs, of which 36 came from boundaries. He completed his sixth Test century off 231 balls. Skipper Mahmudullah Riyad [0*] was at the other end when the bails were drawn.
Bangladesh made three changes in the team, including two debuts. Pace bowler Mustafizur Rahman alongside debutants Mohammad Mithun and Khaled Ahmed replaced Nazmul Hossain Shanto, Nazmul Islam and Abu Jayed.
Electing to bat first, the hosts were in trouble early losing three wickets for just 26 runs in 11.1 overs before Mominul and Mushfiq salvaged the team and took the score to 292/4 in 85.4 overs.
Mominul, the top-scorer of the day, was finally out for 161 off 247 balls, including 19 boundaries, after giving a catch to Brian Chari off Tendai Chatara.
Mominul was 98 when he hit Sikandar Raza to the fence and completed his seventh Test century off 150 balls with 12 boundaries.
A consistent run-getter for Bangladesh, Mushfiq followed suit completing his sixth Test century with a single run off Zimbabwean skipper Hamilton Masakadza in the third session when the score was 252/3 in 75.1 overs. He fired eight boundaries in the process.
After the dismissal of Mominul, spin bowler Taijul Islam [4] came in as night-watchman but failed to hold his nerve and was caught behind by Regis Chakabva off Kyle Jarvis. Bangladesh lost fifth wicket at 299 in the 89th over.
Earlier, opening batsman Imrul Kayes edged Kyle Jarvis and was caught behind for a duck off 16 balls in 6.4 overs when the team total was 13. Within a span of three runs, Jarvis struck again as Liton Kumar Das [9] gave Barndon Mavuta an easy catch.
Debutant Mohammad Mithun failed to prove his worth as he too was out for naught—caught Taylor off Tiripanp—leaving the home side reeling with 26/3 in 11.1 overs.
Jarvis captured three wickets for 48 runs while Tendai Chatara[1/28] and Donald Tiripano[1/33] shared two for Zimbabwe.
Brief score:
Bngladesh 1st innings: 303/5* in 90 overs, at stumps; Mominul Haque 161, Mushfiqur Rahim 111*, Mahmudullah Riyad 0*; Kyle Jarvis 3/48, Tendai Chatara 1/28, Donald Tiripano 1/33.