Afif, who hit seven fours and a six, scored at a steady pace but Rasooli struggled initially, scoring just 19 runs in 25 balls. But the Afghan added 37 runs in the next eight balls to end the match in a whirlwind manner.
Earlier in the day, Dhaka failed to post a big score after winning the toss. Their openers Mizanur Rahman and Usman Ghani took a steady approach and shared a 60-run partnership that took 56 balls.
Usman improved his strike rate before being dismissed for 47, while Nasser Hussain and Ariful Haque scored 30 and 29 from 22 and 18 balls respectively, but it proved not to be enough in the end.
With the win, Chattogram now has four points from four matches while Dhaka has two points from three.