Debutant Brandon Mavuta plundered four wickets as Zimbabwe skittled Bangladesh for just 169 to claim their first Test victory since 2013 and first away from home in 17 years.
Mavuta took 4-21 as the tourists won the first Test in Sylhet by 151 runs - their first away success since winning in Bangladesh 2001 - with a day to spare, the victory Zimbabwe's first in the format since defeating Pakistan in Harare in 2013.
Sikandar Raza did the early damage after the home side had reached 56-0 in their pursuit of 321 for victory.
The off-spinner removed openers Liton Das and Imrul Kayes and then claimed the scalp of Bangladesh skipper Mahmudullah during a 17-over spell which cost 41 runs.
Only Kayes with 43 and Ariful Haque, who was the last man out when he fell to Wellington Masakadza following a quick-fire 38, provided genuine resistance as Bangladesh, who had resumed day four on 26-0, fell well short in the end.
The second Test of the two-match series begins in Dhaka on November 11.