Yasir broke a 52-run opening stand between Tamim Iqbal and Imrul Kayes just before the break after the hosts won the toss and elected to bat on the slow wicket at the Sheikh Abu Naser Stadium.
Tamim fell for 25 as Azhar Ali took a sharp catch at forward short-leg in the second over of Yasir, who had missed the preceding limited-overs series due to injury.
Kayes survived a strong leg-before appeal off the third ball of the innings from Junaid Khan, as the TV umpire turned down Pakistan's review.
Mohammad Hafeez dropped Tamim at leg slip off left-arm spinner Zulfiqar Babar when he was on 16.
Bangladesh handed Test debuts to Soumya Sarkar and fast bowler Mohammad Shahid, while Pakistan picked uncapped batsman Sami Aslam for the opening match of the two-Test series.
Pakistan also ignored senior off-spinner Saeed Ajmal, preferring to go in with two specialist slow bowlers in Zulfiqar and leg-spinner Yasir.
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