Resuming the morning on 32-1 chasing an unrealistic target of 537, Bosch made sure the Proteas got off to the perfect start getting the wicket of Nick Welch for a duck with the first ball of the day.
The seamer, who scored and unbeaten century in South Africa's first innings total of 418-9 declared, then dismissed the dangerous Sean Williams for 26.
Codi Yusuf then came into the attack a made a double breakthrough, the debutant seamer dismissing Wessly Madhevere and Tafadzwa Tsiga to leave the home side tattering on 82-6.
Zimbabwe captain Craig Ervine and number eight Wellington Masakadza then put up some resistance with a partnership of 83 for the seventh wicket.
Masakadza went on to score his maiden half-century in Test cricket but it was unlucky for Ervine as Bosch removed the home skipper for 49 after the lunch interval.
The paceman then completed his five-wicket haul in just his second Test after rattling the stumps of number nine Vincent Masekesa and finished with figures of 5-43 in 12 overs.
Blessing Muzarabani hit two sixes and four fours to be unbeaten on 32 off 29 balls but the match came to an end when leg-spinner Dewald Brevis picked up his first Test wicket as wicketkeeper Kyle Verreynne stumped last man Tanaka Chivanga for the hosts to be 208 all out.
The Proteas now take a 1-0 lead in the two-match series with the second game again being played at the Queen's Sports Club in Bulawayo from Sunday.
Wiaan Mulder hit a career-best 147 as the Proteas were bowled out for 369 in the second innings to set Zimbabwe a mammoth target of 537 with two days remaining of the first Test in Bulawayo.
South Africa lead Zimbabwe by 216 runs at the end of Day Two of their opening Test in Bulawayo.
Lhuan-dre Pretorius became the youngest player to score a Test century for the Proteas to help the visitors recover from 55-4 to post 418-9 at stumps on day one against Zimbabwe in Bulawayo.
Lhuan-dre Pretorius, Dewald Brevis and Codi Yusuf will all make their Test debuts for the Proteas against Zimbabwe in Bulawayo on Saturday, stand-in captain Keshav Mahraj has confirmed.
