Electing to bat first at the Sheikh Abu Naser Stadium, the hosts could not score freely, but Mominul, Imrul Kayes (51) and Mahmudullah (49) made sure they made slow but steady progress.
Shakib Al Hasan was unbeaten on 19 at the close.
Beaten in all four limited-over matches ahead of the two-Test series, Pakistan spilled five chances in the first two sessions.
Tamim Iqbal (25) and Imrul put on 52 for the opening wicket before they were separated by leg-spinner Yasir Shah.
Azhar Ali took a bat-pad catch at short leg to remove Tamim who could have been dismissed earlier if Mohammad Hafeez had held a low catch in the slips.
Imrul had received two reprieves by the time Bangladesh went to lunch at 60 for one.
Pakistan's mediocre catching continued in the second session when left-arm spinner Zulfiqar Babar dropped a return chance offered by Mominul while a Mahmudullah edge flew between the slip fielders.
Hafeez, cleared to bowl again last week after being suspended for an illegal action, caught Imrul off his own bowling, one ball after the batsman had brought up his second Test fifty.
Mominul found an ally in Mahmudullah who dominated their 95-run stand for the third wicket without managing to claim his 12th Test fifty.
Mahmudullah went when he edged Wahab Riaz and keeper Sarfraz Ahmed took a smart one-handed catch.
Mominul then added 49 runs with all-rounder Shakib but was beaten by a turning delivery from Babar that trapped him lbw.
Bangladesh reviewed the decision but could not get it overturned and Mominul fell after a 162-ball innings that included eight boundaries.
Mohammad Shahid and Soumya Sarkar made their test debut for Bangladesh while Pakistan handed a maiden Test cap to Sami Aslam.
Scorecard
Bangladesh (1st innings):
T. Iqbal c Az. Ali b Shah 25
I. Kayes c&b Hafeez 51
M. Haque lbw b Babar 80
Mahmudullah c S. Ahmed b Riaz 49
S. Al Hasan not out 19
Extras: (lb-5, nb-7) 12
Total: (for 4 wickets, 89.5 overs) 236
Fall of wickets: 1-52, 2-92, 3-187, 4-236
To bat: M. Rahim, S. Sarkar, S. Hom, T. Islam, R. Hossain, M. Shahid
Bowling: J. Khan 16-2-40-0(nb-2), W. Riaz 19-5-40-1(nb-1), M. Hafeez 15-5-38-1, Z. Babar 21.5-3-55-1, Y. Shah 18-1-58-1.
Image: Mominul Haque of Bangladesh.
Photograph: Reuters
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