After Shadman Islam (93) and Mominul Haq (50) steadied the innings, Mushfiqur Rahim and Litton Das forged an unbroken 98-run stand for the sixth wicket to keep Bangladesh in the contest.
Bangladesh finished day three 132 behind but will expect Mushfiqur (55) and Litton (52) to help erase the deficit when they resume on Saturday.
Resuming on 27 for no loss, the Bangladesh openers found runs were not easy to come by as the Pakistan fast bowlers, particularly Naseem Shah, bowled with great discipline.
Naseem was finally rewarded when wicketkeeper Mohammad Rizwan flew to his left to take a stunning one-handed catch after Zakir Hasan (12) had slashed hard at the ball.
Khurram Shahzad squeezed one through the bat-pad gap of Bangladesh captain Najmul Hossain Shanto (16) to reduce the visitors to 53-2.
Shadman combined with Mominul in a 94-run stand to dispel fears of any collapse but his second test hundred did not materialise.
After Khurram removed Mominul, Mohammad Ali ended Shadman's 183-ball vigil by bowling him through the gate. The opener hit 12 fours.
All-rounder Shakib Al Hasan made a quick 15 runs before hitting a delivery from Saim Ayub straight to Pakistan captain Shan Masood at extra cover.
Mushfiqur and Litton, however, looked comfortable on a pitch where bowlers from both sides have had to toil for success.
Pakistan tried a short-pitch barrage against Litton, who plundered 18 runs from a Naseem over that included three fours and a six en route to his 52-ball fifty.
