Fresh from ending a run of over a year without an ODI victory in Friday's 87-run triumph, Bangladesh took a 2-0 lead in the five-match series in Sunday's second rubber in Chittagong.
Iqbal (76) and Anamul (80) were a key part of the success, the duo combining for 158 - the second highest opening stand in the country's ODI history - as Bangladesh posted 251-7 from their 50 overs.
One area of concern for the hosts, though, will be the collapse thereafter as Bangladesh dropped six wickets for just 46 runs to fall from 158-0 to 204-6.
However, Zimbabwe, who made just 194 in Friday's loss, saw their problems with the bat continue, Solomon Mire's maiden ODI 50 proving the only bright note as Arafat Sunny (4-29) and Mashrafe Mortaza (3-34) did their part in helping dismiss the tourists for 183.
Bangladesh won the toss and opted to bat first and that decision proved wise with Iqbal and Anamul setting themselves well at the crease, the former having particular joy through cover and point.
Zimbabwe finally made the breakthrough with the final delivery of the 33rd over when Iqbal was run out by a direct hit from Elton Chigumbura.
Shakib Al Hasan, a centurion in Friday's win, was dismissed for a golden duck when he was bowled by Vusi Sibanda from the next delivery and Anamul's disciplined innings came to an end courtesy of the same bowler soon after.
From there Bangladesh lost wickets with regularity, Sabbir Rahman (0), Mahmudullah (12) and Mushfiqur Rahim (27) all falling cheaply, although Mominul Haque boosted the total with an unbeaten 33 from 38 deliveries.
Zimbabwe's reply started badly as Mortaza tore through the top order to dismiss Hamilton Masakadza (0), Sikandar Raza (16) and Sibanda (21), before Sunny got in on the act to account for Brendan Taylor (8) as Zimbabwe were left reeling at 50-4.
Mire held the innings together as he and Regis Chakabva (32) put on 65 for the fifth wicket, the partnership ending when the latter scooped Al-Amin Hossain to Mashrafe at mid-off.
Sunny then took the crucial wicket of Mire and, Chigumbura's 38 aside, the rest of the tail was wrapped up with consummate ease.
Bangladesh will now attempt to wrap up the series in Wednesday's third ODI in Mirpur.