Chasing 117, the Proteas reached 117/4 in just 13.1 overs, with Bosch dominating the Zimbabwe attack with 11 fours and three sixes.
The 33-year-old registered her sixth T20I half-century and first since the 2024 World Cup semi-final against Australia. Promoted to No.3, she shared a 68-run second-wicket partnership with Nondumiso Shangase, who made 18 from 22 balls.
South Africa lost wickets late in the chase, with Faye Tunnicliffe bowled by Michelle Mavunga before Bosch was trapped lbw by Nyasha Gwanzura while attempting a reverse sweep with one run needed. The match was settled when Christine Mutasa bowled a wide.
Earlier, Zimbabwe struggled after choosing to bat, losing four wickets for 20 runs inside the opening four overs.
Nthabiseng Nini enjoyed a dream international debut, taking three wickets as she tore through the Zimbabwe top order. The 21-year-old became only the second South African woman to take a wicket with her first international delivery, following Chloe Tryon.
Nini finished with 3/17 from 3.3 overs, while Kayla Reyneke also claimed three wickets for 29 runs. Annerie Dercksen took 2/15 and Eliz-Mari Marx was the most economical, finishing with 1/9 from three overs.
Modester Mupachikwa's 36 from 43 balls and Michelle Mavunga's 21 from 18 helped Zimbabwe recover from their poor start and reach 116.
The defeat came in Mark Coles' first match as Zimbabwe coach. His side will look to respond in the second match, while South Africa will aim to extend their series lead to 2-0.
India earned their highest-ever T20I run chase when they successfully chalked off New Zealand's 225/4 with four wickets remaining in a run-soaked encounter in Christchurch on Thursday night.
Less than eight overs were bowled in the fifth and final T20I between India and West Indies as heavy rain fell in Bengaluru.
India regained the lead in their five-match T20 international series against the West Indies after Abhishek Sharma's explosive half-century and a disciplined bowling performance secured a 14-run victory in Indore on Sunday.
Monday's AFCON 2027 qualifying action saw DR Congo defeat Zimbabwe, Burkina Faso and Equatorial Guinea earn tight wins, and Tunisia battle to a draw with Botswana.
