Zimbabwe took the early ascendancy in the contest when Bangladesh were bowled out for just 140 in the first innings with 20-year-old left-arm seamer Newman Nyamhuri taking 4-61.
The home team then hammered home their advantage when they racked up a total of 410 with Kaia striking a 140 for a first Test hundred in just his second game.
The opening batter was well supported with Craig Ervine hitting 60, Brian Bennett 59 while Wessly Madhevere was 77 not out as Zimbabwe showed what could be done with a bit of application with the willow.
Facing a hefty deficit of 270, the visitors did not put up he fight expected with the bat as they folded to be 185 on the third day with lanky fast bowler Blessing Muzarabani taking 4-65 in 17 overs.
It is the first time Zimbabwe have completed back-to-back innings victories having also beaten Afghanistan by an inning and 73 runs in what was their last game in the format in October last year.
The teams will now prepare for a three-match ODI series that starts in Harare on 6 July which will then be followed by three-match T20I series.
The South African Women were made to work hard for runs as they eventually chased down 117 to defeat Bangladesh by four wickets in the Women's T20 World Cup at Lord's on Sunday.
Matt Renshaw struck a career-best 89 not out from 52 balls to help Australia beat Bangladesh by seven runs in the second T20I as the visitors took an unassailable 2-0 lead in the three-match series.
Joel Davies starred with the ball on international debut to help Australia beat Bangladesh by four wickets in the first of three T20Is in Chattogram on Wednesday.
Bangladesh ODI captain Mehidy Hasan Miraz says healthy competition in the squad and a conscious effort to prepare better pitches at home has contributed to their improved form.
