Shanto's knock, which included seven boundaries, helped Bangladesh reach 4-194 in their second innings with an overall lead of 112 runs, before bad light forced an early stumps on Tuesday.
Jaker Ali was also unbeaten at stumps on 21 not out.
After the entire first session was washed out due to a wet outfield, Bangladesh resumed on 1-57 - still 25 runs behind Zimbabwe - and appeared to be in control thanks to Shanto and Mominul Haque.
But Zimbabwe struck back with the wickets of Mominul - who made 47 after scoring 56 in the first innings - and Mushfiqur Rahim.
Shanto and Ali stabilised the innings and have shared a 39-run partnership for the fifth wicket.Â
Bangladesh were dismissed for 191 in their first innings and trailed by 82 runs after the tourists replied with 273.
Fast bowler Blessing Muzarabani ended the day with 3-51. He struck in the seventh over on Tuesday, dismissing Mahmudul Hasan Joy for 33 off a short-pitched delivery.
Paceman Victor Nyauchi (1-28) was rewarded for his excellent line and length by dismissing Mominul after forcing him to play and edge behind. Mominul hit six fours in his 84 ball-47.
Veteran Rahim, who came to the crease without a 50 in his past 11 innings, struggled against Zimbabwe's pace.
He eventually nicked a back-of-length delivery from Muzarabani to first slip and was out for just four.
Zimbabwe sensed a chance to dominate Bangladesh again, but Shanto and Jaker successfully resisted to keep the game in the balance.
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