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 Tigers will also need to find a way to dismiss Brendan Taylor cheaply, after he became just the third Zimbabwean to score back-to-back centuries in a Test match.
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.