After Shafiul Islam's strikes put Zimbabwe on the back foot early in their chase of 270, Ziaur's five for 30 snuffed out any hope of a revival as the hosts were bowled out for 148.
The third ODI match between Pakistan and Bangladesh saw as many as 11 spinner being used by both teams.
Shakib Al Hasan bagged four wickets to set up Bangladesh's consolation eight-wicket victory over the West Indies in the third and final one-day international on Tuesday.
It's not often that a match-winning performance on the cricket field gets overlooked when adjudicators decide man of the match awards. But it has happened three times to Bangladesh seamer Shafiul Islam in this World Cup, each time the award going to batsmen who are as surprised as team-mates and fans alike by the choice.