After comfortable victories in Chittagong to move 3-0 ahead in the five-game rubber, the hosts were once again dominant in Dhakha, triumphing by 124 runs.
Anamul constructed a well-paced 95 from 120 deliveries, including nine boundaries, though a safety-first approach from the opener had threatened to leave Bangladesh short at one point.
When Anamul departed in the 36th over with Bangladesh at 167-3, a boost was required and duly arrived thanks to Shakib Al Hasan (40) and Mushfiqur Rahim (33) getting the pedal down for a 72-run union from a mere 48 balls.
Eventually reaching 297-6, Bangladesh then removed Zimbabwe's top three - shorn of Sikandar Raza due to a broken finger - within the first 10 overs and never looked back, cruising to a first ODI series win of 2014 as the tourists were all out in 39.5 overs.
Whitewashed in the recent Test series, this defeat was Zimbabwe's worst at the hands of Bangladesh in the shortest format, but stifling early bowling had initially raised hopes of a rare success.
Though Anamul and Tamim Iqbal (40) put on 121 for the first wicket, it took half the innings to compile, and Mominul Haque (15) failed to contribute much after Tamim had been run out while chasing a second.
Approaching a fourth ODI century, Anamul fell five runs short as he lofted a full toss from Tafadzwa Kamungozi (3-31) to sub fielder Shingi Masakadza at deep midwicket.
That brought Shakib and captain Mushfiqur together, though, and their rapid-fire partnership put Bangladesh into a dominant position, built upon further by late hitting from Mahmudullah (33 not out) and Sabbir Rahman (22).
Wickets fell regularly as the tourists chased down an unlikely victory target, a task made near impossible as Vusi Sibanda (9), Hamilton Masakadza (12) and Timycen Maruma (8) got Zimbabwe off to a terrible start.
Elton Chigumbura's unbeaten 53 was the sole highlight of Zimbabwe's knock, but the number seven batsman was afforded no assistance from the tail.
And a dismal day for the visitors was wrapped up as last man Kamungozi was bowled by Bangladesh's star with the ball, Arafat Sunny, who took four wickets for the second game in a row.