A second-half strike from Thapelo Maseko in the 63rd minute proved enough to give Bafana Bafana victory at Estadio Monterrey in Guadalupe, Mexico.
The win saw South Africa finish second in the group and qualify for the knockout stage for the first time in their history.
The result marked an impressive recovery for Hugo Broos’ side, who began their campaign with a disappointing 2-0 defeat to Mexico.
After the match, the South African coach described the achievement as a way of proving doubters wrong.
South Africa will now face Canada in the Round of 32 on Sunday.
Canada also made history by reaching the World Cup knockout stage for the first time after finishing second in Group B.
In Group C, Morocco bounced back from an early setback to beat Haiti 4-2.
Haiti shocked the Atlas Lions with an early goal following a mistake by goalkeeper Yassine Bounou, while Isidor later added another.
Morocco responded strongly, with goals from Achraf Hakimi, Ismael Saibari, Soufiane Rahimi and Gessime Yaccine completing the comeback victory.
The North Africans ended the group stage with seven points, level with Brazil but behind on goal difference.
Brazil claimed top spot after defeating Scotland 3-0, following a brace from Vinicius Jr and another goal from Matheus Cunha.
Morocco secured a knockout clash against the winners of Group F, where the Netherlands, Japan and Sweden are still battling for first place.
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