Shahzad ripped through the top order with 4-15 and fellow quick bowler Mir Hamza took 2-29 as Bangladesh collapsed to 26-6 in reply to Pakistan's first innings 274 in the rain-affected match which saw Friday's first day washed out.
At the break, Mehidy Hasan Miraz was on 33 and Litton Das 13 as the pair fought to repair the innings with a dogged unbroken seventh-wicket stand worth 49.
Mehidy has hit seven fours so far in his gritty 48-ball knock but Bangladesh still need another 49 runs to avoid the follow-on with four wickets remaining.
Bangladesh resumed on 10-0 but Shahzad soon had opener Zakir Hasan caught by Abrar Ahmed at short midwicket for one in the fourth over.
Shahzad then bowled Shadman Islam (10) and skipper Najmul Hossain Shanto (1) in the space of four deliveries to reduce Bangladesh to 20-3.
At the other end Hamza had Mominul Haque caught by Mohammad Ali at mid-on for one and then removed first Test centurion Mushfiqur Rahim for three, caught behind by Mohammad Rizwan from a beautiful outswinger.
Shahzad made it 26-6 by trapping Shakib Al Hasan lbw for two before Mehidy and Das dug in.
Bangladesh lead the two-match series 1-0 after winning the first Test, also in Rawalpindi, by 10 wickets -- their first win in 14 matches against Pakistan.
