Much could rest on how the two keepers do, Taylor and Taibu. They're two of the better Zimbabwe batsmen, thereafter it will just be Ervine (34.69 in ODIs), Chigumbura (14.77 in 7 Tests, 23.91 in ODIs) and the tail.
50s each for Taylor and Taibu, Zimbabwe are easing into a strong position from which to strike for victory. 202/4 at the moment, a lead nearing 300 and the bangles will have to hope the second new ball will see the target restricted to something close to 300 and not nearer 350 or 400.
That new ball battle, assuming Zimbabwe don't collapse, could prove the do or die point of the match although I feel the bangles are already up against it needing to better their 1st innings total to win and it could be closer to Zimbabwe's 1st innings total unless they finish Zimbabwe off.
Time for a bit of statistics looking up for matches in Zimbabwe and involving Bangladesh.
Bangladesh
Highest run chase = 217/6 vs West Indies (2nd XI)
HowSTAT! Match Scorecard
Tests won : 3
vs Zimbabwe in Bangladesh
vs West Indies in West Indies (2nd XI, 2x wins)
Harare SC (27 Tests)
ZIM 2-0 BAN (8 wkts/183 runs)
Wins : Home 5-13 Away
Highest run chase = 192/7 (Pakistan vs Zimbabwe 97/98)
All pretty much points to a home win, bar the away record of teams but Bangladesh have lost both visits to Harare so I think what other countries do is irrelevant to a country that has only won three times in its Test existence and two of them against a second string West Indies side. And Bangladesh have lost 60 Tests having yet to play 70, Zimbabwe have won eight and lost only 50 of over 80 Tests.