Breakaway Springbok flanker Juan Smith underlined the relief and satisfaction of his side following their jittery 14-10 success against Scotland at Murrayfield on Saturday.
The world champions made it two wins from two on their tour of the home nations after last week's win in Wales thanks to Jaque Fourie's well-worked second-half try and three Ruan Pienaar penalties.
The Scots had been in control at 10-0 ahead just after the half-time break - only for the tourists to regroup and hit back in ultimately decisive fashion.
Scotland had chances to win at the end but can be buoyed by a hugely improved performance from last weekend's 32-6 loss to New Zealand.
"All credit to Scotland for their excellent performance, however we came back well after a poor opening period," said man-of-the-match Smith.
"Scotland battered away at us for the full 80 minutes, but once we had found our structure, we felt we were okay.
"And our defence held up strongly when they had us under pressure in the last 10 minutes."
South Africa visit England in a rematch of last year's World Cup final next week while Scotland host Canada.
"It is going to be a tough one," Smith said about the encounter at Twickenham.
"We haven't played our best rugby till now, but as I said it is all preparation for us for the British & Irish Lions tour for next year, so we are looking forward to getting three wins on tour."
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