Bangladesh, 1-0 down in the two-Test series and put in to bat, limped to 88 for five in 37.1 overs.
Play had started an hour before lunch under gathering storm clouds, after the first two days were wiped out without a ball being bowled because of a wet outfield.
Bangladesh openers Hannan Sarker and Shahriar Hossain survived a testing spell of fast bowling by Zimbabwe captain Heath Streak to reach the interval on 24 without loss.
They took 51 balls, however, to score their first runs off the bat as Streak and medium pacer Douglas Hondo generated swing through the air and seam movement off the pitch.
The pair upped the tempo in the afternoon and had put on 64 for the first wicket before Hossain drove at a wide delivery from fast bowler Ervine and was caught behind by wicketkeeper Tatenda Taibu for 31.
Threeovers later, Habibul Bashar drove at a Streak outswinger to be caught by Travis Friend in the gully for four.
Bangladesh, who have lost a record 21 Tests in a row, then slipped to 73 for three two balls later when Sarkar was bowled around his legs by Ervine for 25.
Mohammad Ashraful scored one before driving at a delivery from fast bowler Friend and was caught, after a juggle, by Stuart Carlisle at first slip.
Seven balls before rain halted play, Rajin Saleh edged a drive off Hondo to Friend in the gully to depart for six.
At tea, Manjural Islam Rana was five not out with Mushfiqur Rahman yet to score, Ervine ending the session with figures of two for 26 in nine overs