An early try by JP Pietersen, 11 points from the boot of Morne Steyn and a late penalty by Pat Lambie meant France lost at home to the Springboks for the first time since 1997.
Les Bleus went into the match looking for a change of luck after losing three Six Nations games and suffering four consecutive defeats against New Zealand but were immediately on the back foot.
The South African camp said they noticed France captain Thierry Dusautoir and his team were jittery before the game.
"Even at the toss with Thierry you could see they were a bit nervous so we got motivation from that," opposing skipper Jean de Villiers told reporters.
"We got a lucky try at the start and it set us up nicely. We have massive respect for France, we knew it was going to be ugly but we just had to win."
Pietersen charged down Morgan Parra's kick with one minute on the clock to score the early touchdown and Steyn converted.
Parra missed a 30-metre penalty while France, who beat only Scotland and Tonga in 2013, relied too much on flyhalf Remi Tales's kicking and gave the ball away on numerous occasions as they struggled to cope with South Africa's aggressive defence.
The visitors, who whitewashed Scotland 28-0 on Sunday after beating Wales 24-15, went 10 points up with a 38-metre penalty from Steyn and some poor offloads meant France could not respond with their normal bright attacking game.
Steyn added three points with another penalty only for Yoann Huget to give the hosts a lifeline when he dived over in the corner from Parra's pass.
Parra converted to reduce the arrears to six points.
PAPER-THIN DEFENCE
Jaque Fourie touched down early in the second half after De Villiers had run through the paper-thin French defence but it was ruled out for a knock-on.
In the 50th minute Huget stuck out an arm to touch the ball over his own line and prevent Francois Louw from scoring for the Springboks.
Steyn's third penalty on the hour earned South Africa a nine-point lead before manager Philippe Saint-Andre added beef to the French side by bringing on Mathieu Bastareaud for Florian Fritz.
Hopes of a late comeback sunk in the 68th minute when Thomas Domingo picked up a yellow card for a spear tackle on Bryan Habana.
Huget then made a brilliant darting run for France and caught the defence off guard with a fine kick, only for the rebound to bounce just over his head as he was sprinting for a certain try.
Eight minutes from time Louw was sent to the sinbin for punching Pascal Pape in the scrum, allowing substitute scrumhalf Jean-Marc Doussain to bring the gap down to six points with the resultant penalty.
France followed up with another mistake in their own half and Lambie sealed South Africa's win with a perfectly executed penalty one minute from time.
"We're extremely disappointed because we have the team to beat these kind of nations but we committed too many fouls," said Dusautoir.
(Editing by Alan Baldwin and Tony Jimenez)
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