Published: 2020-02-09 19:36:50 BdST
Naseem, who turns 17 next week, removed Najmul Hossain, Taijul Islam and Mahmudullah before Bangladesh finished day three of the opening Test on a precarious 126-6 and staring at an innings defeat.
Having conceded a first-innings lead of 212, Bangladesh were showing signs of fight as they reached 124-2.
Bassem hit Najmul on the thigh pad with a moving delivery, and although the lbw appeal was turned down, Pakistan captain Azhar Ali opted to review the umpire's decision and replays confirmed the ball would have hit the stumps.
Nightwatchman Taijul also fell lbw and Mahmudullah edged the next ball to Haris Sohail who took a smart low catch at slip as Naseem became the fourth Pakistani to claim a Test hat-trick after Wasim Akram (twice), Abdul Razzaq and Mohammad Sami.
Pakistan were all out for 445 in their first innings.
Babar Azam could not add to his overnight score of 143 and fell to the first ball of the day
Asad Shafiq was out for 65 and Haris made a fluent 75 while Abu Jayed and Rubel Hossain claimed three wickets apiece for Bangladesh.