Mpofu claimed a career best four wickets for 42 runs in his 12th match while left-arm spinner Dabengwa bagged his best of three for 19 runs in his eighth appearance.
Put in to bat by Zimbabwe captain Prosper Utseya, who won the toss, Bangladesh started confidently in the day-night match until opener Shahriar Nafees (35) was removed by Elton Chigumbura, who bowled just the one over.
Nafees was caught by Gary Brent at short fine leg on the fourth ball of the 10th over to break an opening partnership of 64 runs with Mehrab Hossain jnr, the top scorer with 38.
Nafees played 34 balls and hit seven fours while Mehrab delighted the home crowd with five fours from 77 balls played. Mohammad Ashraful (36), Saqibul Hasan (26), Mashrafe Mortaza (23 not out) were other contributors.
Brent and Utseya also took one wicket for 42 and 21 runs respectively.
Bangladesh lead the five match series 2-0.
Bangladesh 220 all out (S Nafees 35, M Hossain 38, Mohd Ashraful 36; Mpofu 4 for 42, Dabengwa 3 for 19) Vs Zimbabwe (yet to bat)