Shanto, batting at number 4, struck 101 from 130 balls while Mominul Haque scored 91 as the home team went to stumps on 301-4 after being sent in to bat at the toss.
Pakistan had initially made a double breakthrough early onto reduce the hosts to 31-2 with Shaheen Shah Afridi dismissing Mahmudul Hasan Joy (8) and fellow seamer Hasan Ali getting rid of Shadman Islam (13).
Shanto and Mominul then combined for a partnership of 170 for the third wicket to rebuild before the stand was broken on the stroke of the tea interval when the latter was lbw to left-arm spinner Noman Ali.
The skipper was then joined by the experienced Mushfiqur Rahim and the pair added 75 before Shanto was trapped in front by seamer Mohammad Abbas aftee scoring his ninth Test hundred.
At 276-4, Pakistan might have hoped for a good end to the day but Mushfiqur made his to way to 48 not not and Litton Das (8 not out) made sure there was no further loss of wickets.
Bangladesh captain Najmul Hossain Shanto said fierce competition within the side's bowling unit had become the driving force behind their historic 2-0 Test series sweep over Pakistan after a 78-run victory in Sylhet on Wednesday.
Cricket Australia have made several bold calls in the announcement of their touring squad for six ODIs and three T20Is in Pakistan and Bangladesh.
Pakistan's two debutants, Azan Awais and Abdullah Fazal, showed good composure with the bat on the second day as the visitors made a strong reply after Bangladesh were bowled out for 413 in the first Test.
Australia are set to be missing several key personnel when they tour Pakistan for three ODIs starting later this month.
