Heavy downpour allowed 63.2 overs of play, which is a significant improvement over nearly-washed out Day 2 and 3 at the Sher-e-Bangla National Cricket Stadium on Tuesday.
Pakistan lost the wickets of Babar Azam (76) and Azhar Ali (56) early in the day but Mohammad Rizwan (53) and Fawad Alam (50) paired in a century stand before the tourists declared with a day and a half in hand.
He began with the wicket of debutant Mahmudul Hasan Joy, who fell for a duck after attempting to take the fight to the bowlers. Shadman Islam (3) followed for a catch at point to Hasan Ali, who then ran skipper Mominul Haque (1) out.
After surviving a close lbw shout, Mushfiqur Rahim (5) swept Sajid straight to Fawad at short midwicket. Sent ahead of Shakib Al Hasan, Liton Das (6) also tried to attack the bowlers but departed for a return catch as Bangladesh slipped to 46 for five.
Shakib and Taijul Islam then saw through 32 deliveries before the umpires called for stumps due to bad light with Bangladesh still trailing by 224 runs in their first innings.
Earlier, Bangladesh began the day with seamer Khaled Ahmed grabbing his maiden Test wicket of Babar in the second over of the day before Ebadot Hossain took out Azhar.
Rizwan and Fawad then stitched up an unbroken 103-run stand as Pakistan declared as soon as the latter reached his half-century.
Rizwan survived three close calls - dropped on 30 and overturning two leg-before decisions on review.