At tea, Ashraful was 59 not out in a total of 191 for five in reply to Zimbabwe's first innings of 441.
Ashraful began his innings aggressively, but soon settled down to face 133 balls and hit seven fours and a six, a fine blow over long off off left arm spinner Ray Price that took him to his half-century.
Bangladesh, who resumed on 14 for one, lost their second wicket in the sixth over of the day's play when Tapash Baisya drove at a delivery from pace bowler Heath Streak and was caught behind for four by wicketkeeper Tatenda Taibu.
Three balls later Bangladesh slumped to 35 for three when fast bowler Andy Blignaut had Habibul Bashar caught behind by Taibu for a duck.
Opener Shariar Hossain and Rajin Saleh stabilised the innings with a cautious partnership that took Bangladesh to within sight of lunch without further loss.
But 12 overs before the end of the morning session Hossain was lbw to medium pacer Douglas Hondo for 48 to end the fourth-wicket stand at 42.
Saleh continued to bat responsibly, sharing a stand of 85 for the fifth wicket with Ashraful.
The partnership ended an hour before tea when Saleh (49) attempted to sweep a full delivery from Price, who was bowling over the wicket, and gloved it on to his stumps.
Mushfiqur Rahman, who was 14 not out, helped Ashraful add 29 runs for the unbroken sixth wicket.
Bangladesh might have dismissed Mushfiqur for six with the total 182 for five in the seventh over before tea but Price failed to hold on to a hard-hit return catch.
