The Springboks outscored their opponents three tries to nil with Zane Kirchner, Marcell Coetzee and Bryan Habana the men to cross, while fly-half Morne Steyn contributed 12 points from three conversions and two penalties for the hosts.
Argentina, making their long-awaited debut in the southern hemisphere's new-look tournament, responded with two first-half Juan Martin Hernandez penalties but they never looked likely to cause an upset in Cape Town.
South Africa's victory sees them move above New Zealand in the standings, with the All Blacks having beaten Australia 27-19 in the Sydney earlier today.
Steyn, who in making his 38th Test appearance for his country passed Butch James' mark as South Africa's most-capped fly-half, opened the scoring in the third minute when he slotted over a penalty following a threatening attack that almost brought the home side a try.
Hernandez drew the visitors level 11 minutes later with a penalty of his own but South Africa responded with the opening try of the match from Kirchner.
The fullback, who conceded the penalty that allowed Hernandez to make it 3-3, made the most of good work by Steyn to cross on the left, with Steyn adding a fine conversion.
Steyn continued his 100% record with a straightforward penalty in the 25th minute to make it 13-3, before the Springboks scored their second try two minutes later when 21-year-old Coetzee crossed for his first international try.
Steyn tagged on the extras and although Argentina reduced the arrears almost immediately with Hernandez's second penalty of the match, South Africa held a 20-6 advantage at the break.
Heyneke Meyer's side would have been hoping to push on from there in the second half and get the bonus-point victory, but they could only add seven more points through record tryscorer Habana's converted 57th-minute score.
After Hernandez had three penalties at the start of the second half that could have put Argentina right back in the contest, Habana collected Steyn's superb cross-field kick before touching down his 41st international try.
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