Worse followed for Argentina when a mistake helped set up a third Springbok try on the stroke of half-time.
Juan Martin Hernandez dropped a ball in midfield.
Steyn seized on the chance and found fellow center Fourie, who released to the onrushing Schalk Burger. The flanker then delivered a try-scoring pass to No. 8 Rossouw.
Argentina then caught South Africa cold with a controversial try early in the second half.
After working an overlap, Manuel Contepomi dived over the line under a challenge from Montgomery.
Referee Steve Walsh asked replay official Tony Spreadbury to check the grounding. From one angle it looked as if the outside center had lost control but Spreadbury, himself an experienced Test referee, confirmed the try.
Felipe Contepomi converted his twin brother's score and South Africa's lead had been cut to 24-13. But he then missed a penalty which, had it gone over, might have rattled Springbok nerves.
Two more Montgomery penalties removed any doubt over the result before Habana, intercepting a Hernandez pass, ran some 80m for a flamboyant try under the posts four minutes from the finish.
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