Anamul finished on 73 off 62 balls while Mushfiqur Rahim, who returns to the national team after skipping the West Indies tour for hajj pilgrimage remained unbeaten on 52 off 49 balls.
Zimbabwe bowlers had a power day at the office after their stand-in skipper Regis Chakabva opted to bowl first after winning the toss.
The hosts tried out eight bowlers in the innings, of which only Sikander Raza and Victor Nyauchi managed to get into the wicket’s column, picking up one wicket each.
Bangladesh took charge of the match from the start, with the opening stand of Tamim and Liton taking the score to 51 without any loss after the first 10 overs.
The run-rate dipped a little in the next 10 overs, with Tamim, who began the match with 7943 runs in the format, batting with a bit more caution as he approached his fifty and the milestone of 8,000 ODI runs.
The left-hander finally reached the milestone in the 24th over, by hitting a boundary off Sikander Raza.
Tamim is overall the 33rd player in ODI history to score more than 8,000 runs. He is also the ninth opener in history to reach the milestone.
Tamim tried step on the accelerator after reaching the milestone, but his attempt to slog a short delivery off Raza backfired, as he ended up top-edging the ball and giving an easy catch at fine-leg.
Anamul, who last played an ODI for Bangladesh in July of 2019, then joined Liton Das.
Liton looked a bit edgy early on in his innings but finally found his groove by hitting Wellington Masakadza for a hat-trick of boundaries in the 30th over.
It took Liton 75 balls to reach his half-century. In the next 14 balls he faced, Liton smashed five fours and one six to score 31 runs.
But Liton’s innings ended abruptly. After completing a quick single, Liton went to the ground, clutching his knees and looked to be in tremendous pain. The opener then had to be taken off the field on a stretcher.
Anamul started from where Liton left off, taking on the Zimbabwe bowlers, hitting six fours and three sixes to put Bangladesh on course for 300.
Anamul was dropped on 71 by Wessly Madhevere in the deep off Ngarava in the 45th over. But he couldn’t cash in on the second life, as he got caught by Tarisai Musakanda at long-on off Victor Nyauchi in the very next over.
Bangladesh was on 281-2 after 47 overs. But Mushfiq and Mahmudullah (20* off 12) could only score 22 runs off the final 18 deliveries, which could prove to be costly later in the match.