Argentina led for much of the encounter after tries from flanker Juan Manuel Leguizamon and centre Marcelo Bosch, but Pumas indiscipline in the final 10 minutes allowed South Africa to edge ahead and hold on for victory.
Bjorn Basson scored the visitors only try, with Steyn kicking the rest of his side's points to take them to the top of the four-nation tournament standings on points difference from title holders New Zealand.
(Reporting by Nick Said in Cape Town; Editing by Rex Gowar)
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