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SA will now go into a play-off match for 9th and 10th place with the opposition yet to be confirmed.
The South Africans could finish their campaign off as the best Olympics yet if they manage a second victory at the global shopiece.
It was the team's first victory at the Games after they suffered four defeats against Australia, New Zealand, Argentina and Germany.
They were in an unforgiving mood as they led the US women 4-0 at the half-time break and almost double their efforts in the second half with three goals.
Athlete Andre Olivier automatically qualified for the men's 800m semi-final after finishing third in his heat, with a time of 1:46.42.
Olivier finished behind the United States' Duane Solomon (1:46:05) and the Netherlands' Robert Lathouwers, who crossed the line in 1:46:06.
The semi-finals will take place on Tuesday.
