The hosts took a 152-run lead without losing any wicket in the second innings. Jubair finished with his maiden five-wicket haul when he dismissed Mushangwe in the 106th over, bowling out Zimbabwe for 374.
After losing the first wicket early, fine fifties from Hamilton Masakadza and Sikandar Raza helped Zimbabwe steady their innings. Bangladesh bounced back by picking up three quick wickets just before lunch.
However, Chakabva and Chigumbura combined well in the second session to form a century partnership and help Zimbabwe avoid the follow-on.
The problem for the visitors was that they kept losing wickets in clusters and hence were unable to go past Bangladesh's score. All will depend on how Brendan Taylor uses his pacers now as Bangladesh will play 8 overs before close of play.
It is a day of sheer dominance from Bangladesh as the Bangladeshi bowlers have struck for Tigers, sending the visitors in a lot of trouble.
With a handsome deficit lying ahead of them, Zimbabwe scored 374 runs, losing all wickets.
Zimbabwe's top order came good to put up a strong reply to Bangladesh's huge first innings total of 503 on the second day of the third and final Test in Chittagong.
But for Bangladesh, Jubair, Shafiul and Shakib bowled very well while Taijul, though bowling some impressive deliveries that turned and bounced to trouble the batsmen, were slightly more expensive.
