The talented 23-year-old left-hander batted fluently to cross 50 for the 12th time in his first 13 Tests before being trapped leg-before by Zulfiqar Babar off the last ball of the day.
Opener Imrul Kayes made 51, Mohammad Mahmudullah scored 49 and Shakib Al Hasan was unbeaten on 19 after the hosts elected to take first strike in good batting conditions at the Sheikh Abu Naser Stadium.
Mominul has scored a half-century or more in his last 10 Tests. Only four batsmen -- Viv Richards of the West Indies, South Africa's AB de Villiers and the Indian duo of Gautam Gambhir and Virender Sehwag -- have scored more 50s in consecutive Test matches.
Leg-spinner Yasir Shah, off-break bowler Mohammad Hafeez, left-arm seamer Wahab Riaz and left-arm spinner Zulfiqar claimed a wicket each, but Pakistan were let down by shoddy catching and fielding.
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The most expensive let-off was by Zulfiqar, who spilled a simple return catch when Mominul was on 17.
Yasir broke a 52-run opening stand between Tamim Iqbal and Imrul just before lunch by having Tamim (25) caught at forward short-leg by Azhar Ali.