Iqbal (56) and Mashud (51) came up with timely knocks at the Bangabandhu National Stadium as the home side looked to keep their hopes alive in the five-match series, currently led by Zimbabwe 2-1.
Electing to bat, Bangladesh established the basis for a competitive total thanks to Iqbal, who slammed his second half-century of the series and added a useful 71 for thesecond wicket with Aftab Ahmed (44).
The 20-year-old, who had scored 58 in the second one-dayer at Chittagong earlier this week, struck six fours and a six during his 76-ball innings before he was caught byStuart Matsikenyeri at long-on off spinner Prosper Utseya.
Mashud later took control of the proceedings with a well-paced 62-ball knock, containing a six add two fours. Mashud, who got to his sixth one-day fifty with a six off spinner Brendan Taylor, fell off the next ball as he tried another big shot and was caught by Utseya at long-on.
Taylor also bagged the wickets of all-rounders Mohammad Rafique (one) and Khaled Mahmud (zero) to finish with 3-54.