The hosts' win brought the series to 1-1 and also broke a losing sequence that stretched back 13 one-day internationals.
"This was a really good and much needed performance, giving us great morale with which to go into the next match," said Zimbabwe captain Prosper Utseya said.
"Sibanda was outstanding today, as was Brent. But it was essentially an all-round effort."
It was arguably Zimbabwe's most decisive win over their frequent rivals at the foot of the ICC rankings.
And to add injury to insult Mohammad Rafique's face and Sibanda's helmet accidentally clashed in mid-pitch, causing the veteran Bangladeshi all-rounder to leave the field with a bloodied nose for x-rays.
Bangladesh had struggled in their innings to 153 all out, a target which Zimbabwe reached with more than 14 overs in hand.
The tourists had lost their first two wickets for only five runs early in the day after deciding to bat and their seventh wicket fell at 81.
Rafique and Mushfiqur Rahim brought some respectability to the tail-end of the innings with a 56-run partnership. But it was nowhere near enough.
Gary Brent's 4-30 in 10 overs was not quite a career best (4-22) but it was more than enough to bludgeon Bangladesh into submission. At one stage he had captured three weeks for two only runs.
On past performance Zimbabwe might have been expected to also collapse as their record in run chasing has been poor in recent years.
But a solid 31 from Terrence Duffin holding the fort and a spectacular innings of 93 not out by Sibanda took them to a 125-run opening partnership and almost home. Only one more wicket fell in reaching target.
Bangladesh 153 in 46 overs (Mohd Rafique 40, Mushfiqur Rahim 27, Aftab Ahmed 24; Gary Brent 4 for 30, Sean Williams 3 for 23, Mpofu 2 for 26) lost to Zimbabwe 156 for 2 in 35.2 overs ( V Sibanda 93 n o, T Duffin 33; Saqibul Hasan 1 for 29) by 8 wickets