The 23-year-old spearhead removed the home team's skipper Shan Masood for six and then star batter Babar Azam for a two-ball duck before Pakistan launched their recovery on a greenish pitch.
Saim Ayub was unbeaten on 42 and Saud Shakeel on 28 at the break, having added a fighting 65 in their fourth-wicket stand.
Bangladesh skipper Najmul Hossain Shanto took no time in sending Pakistan in to bat after winning the toss and caught Pakistan napping at 16-3.
It was Shoriful's new-ball partner Hasan Mahmud who gave the visitors the first breakthrough when Abdullah Shafique was smartly caught at gully by Zakir Hasan for two in the fourth over.
Shoriful then had Masood caught behind off a sharp delivery, with Bangladesh successfully reviewing a not out decision by South African umpire Adrian Holdstock.
Masood argued the decision by television umpire Martin Gough of England with the on-field officials as Bangladesh fielders celebrated the dismissal, refusing to accept he nicked the ball.
Babar nicked a leg-side delivery in Shoriful's next over and was caught by wicketkeeper Liton Das for his first home-ground duck in 14 Tests.
No play was possible before lunch, with 230 minutes of action lost because some wet outfield patches left by overnight rain were deemed dangerous.
Pakistan entered the Test with four fast bowlers in an all-pace attack with no frontline spinner, while Bangladesh included three pacers and two spinners.
The two-match series is part of the nine-team World Test championship, with Pakistan currently sixth in the standings and Bangladesh eighth.
