Younis made 148 and Azhar was unbeaten on 127, the pair having shared a third-wicket stand of 250 to rescue the tourists from 58-2 after Bangladesh captain Mushfiqur Rahim won the toss and elected to field in Dhaka.
Both batsmen were lucky to reach three figures after being reprieved by no-balls even as Bangladesh struggled to overcome the loss of strike bowler Shahadat Hossain in the day's first over.
Shahadat returned after the morning drinks break, and even though he did not bowl for the rest of the session, he took a catch in the deep to dismiss Sami Aslam.
However, Shahadat broke down again while training during the lunch break and had to be lifted away on a stretcher.
Chief selector Faruque Ahmed said the 28-year-old seamer had injured his right knee and was unlikely to take any further part in the match.
Part-time seamer Soumya Sarkar would have dismissed Younis on 78, caught in the covers from a mistimed drive, but TV replays showed the bowler had overstepped to concede a no-ball.
Similarly, Azhar escaped on 18 when he was caught in the slips off Mohammad Shahid, only to see TV umpire Ranmore Martinesz confirm a no-ball.
Azhar's dismissal at the stage would have reduced Pakistan to 38-2 after Bangladesh had removed both openers cheaply.
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