Opener Tanzid Hasan struck an unbeaten century, reaching 100 off 98 balls with six fours and seven sixes to anchor the innings.
He shared a 105-run opening stand with Saif Hassan, who scored 36 before falling to Shaheen Shah Afridi.
Najmul Hossain Shanto added 27 before being dismissed by Haris Rauf, while Litton Das remained unbeaten alongside Tanzid as Bangladesh reached 177 for 2 in 33 overs.
