He then brilliantly set up JP Pietersen for another in a three-minute period that effectively sealed the match before halftime.
The only try of the second half came through Coenie Oosthuizen as Scotland were kept pointless by the Springboks for the fist time home or away since 1951.
Scotland suffered from a misfiring lineout, losing five throws in the first 40 minutes, while the Boks, who had veteran lock Bakkies Botha playing his first test since the 2011 World Cup, played fluent rugby on the back of a strong forward effort.
The visitors, who beat Wales 24-15 last weekend, dominated early possession and territory, and Scotland had barely touched the ball when they fell behind after four minutes when Alberts drove through weak defence from a lineout.
Scotland slowly dragged themselves back into the contest through dogged defence, but their first real attacking effort was thwarted when Sean Maitland failed to control a pass from Ruaridh Jackson just after the half-hour mark, allowing le Roux to scoop up the ball and race 60 metres to score.
"The ball bounced into my hands and I was lucky to be there to score my try," Le Roux, who plays Super Rugby for the Cheetahs, told the BBC.
"You don't know when it will be your last game so you have to play every game as though it is your last."
Le Roux then turned creator from the restart, easing through a gap in the defence before stepping another attempted tackle and kicking ahead for wing Pietersen, who celebrated his 50th cap by shrugging off the covering defence to score in the corner.
"It is an amazing achievement and to play it at Murrayfield is something I will treasure for the rest of my life," Pietersen said.
"We wanted to step up this weekend and we did that. We executed the game plan well. The conditions didn't suit us but we took the opportunities we had."
Scotland showed more attacking endeavour in the second half despite the poor condition of the pitch but failed to seriously threaten the South Africa line, and they once again paid the price when replacement prop Oosthuizen drove over on the back of another dominant lineout after 52 minutes.
The hosts were boosted by a yellow card to replacement flanker Marcell Coetzee with 10 minutes remaining following a series of infringements, but despite playing with only 14 men the Springboks defence held firm.
David Denton went close to earning Scotland a try but was tackled into the touch by Pietersen, while Max Evans was denied by the outstretched hand of Bryan Habana following a lengthy injury break for flanker Francois Louw, who was taken off by stretcher after contact with Jim Hamilton.
Scotland host Australia in their final November international next week. South Africa take on France in Paris.
(Reporting by Josh Reich, editing by Ed Osmond)
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