Anamul made 80 off 110 balls while Tamim cracked 76 off 98 balls as Bangladesh posted 251-7 before dismissing Zimbabwe for 183 runs in 44.5 overs to take 2-0 lead in the five-match series.
Anamul and Tamim provided Bangladesh the foundation putting on 158 runs in what was the side's second best opening stand after Mehrab Hossain and Shahirar Hossain's 170 against the same opponents in 1999.
Bangladesh suffered a major collapse losing six wickets for 46 runs after Tamim was run out, but Mominul Haque, batting at number seven, guided the score past 250-run mark with an unbeaten 33 off 23 balls.
Solomon Mire top-scored for Zimbabwe with his maiden fifty -- 50 off 79 balls -- while Regis Chakabva (32) and Elton Chigumbura (38) played late cameos but Bangladesh were always in control.
Arafat Sunny, who finished with 4-29, bowled last three batsmen in his final over after Chigumbura was run out by Sabbir Rahman with a direct hit.
Mortaza (3-34) was adjudged man of the match.
Bangladesh won the first match by 87 runs at same venue on Friday.
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