Chris Paterson then dashed clear on the interception to bag what looked like a crucial second score.
But Scotland's glee turned to gloom when referee Tony Spreadbury ruled that winger Simon Webster had committed a knock-on almost a minute earlier close to his own line.
So, instead of awarding Scotland a try, the Boks were given a scrum five metres out - and seconds later, Fourie du Preez wriggled over for a home touchdown.
Scotland boss Frank Hadden had stressed the importance of a strong start, but it was the home troops who raced out of the traps to rattle up six points before five minutes had been played.
They broke the deadlock in just 60 seconds when Percy Montgomery confidently slotted home a 35-metre penalty - and he quickly doubled his tally to put the hosts 6-0 up.
Hadden's brigade shook off their jitters to hit back with a superbly-worked touchdown in the 12th minute, Gordon Ross sending through a perfectly-weighted grubber kick for Webster to pounce in the corner.
Paterson's angled conversion drifted wide of the near post.
It took rattled South Africa just three minutes to reclaim the momentum, Montgomery completing his penalty treble from 46 metres when Gavin Kerr failed to backtrack quickly enough following Ross' midfield chip.
Ross was back in the spotlight midway through the half when he was guilty of illegally handling the ball on the ground.
Jaco van der Westhuizen took over the boot duties - and thumped it over from 55 metres to open up a seven-point gap.
Scotland began the second half well by launching a sequence of promising raids.
But a combination of robust Springboks marking and a lack of penetration prevented them turning pressure into precious points.
Having weathered the storm, South Africa bounced back to increase their advantage through Montgomery when Jonny Petrie was isolated in retreat.
Scotland kept their hopes alive when Paterson banged over a 40-metre penalty in the wake of a crunching challenge by skipper Jason White on Schalk Burger.
The penalty ping-pong duel between the marksmen continued as Montgomery slotted his own fifth and number six for South Africa.
Then came the fateful moments for the Scots - and, although Paterson goaled a sniping score for substitute flanker Donnie Macfadyen, the damage was too severe to repair.