The Springboks made 10 changes to the team that had defeated England the week before and, with a relatively inexperienced side, were there for the taking.
But a wasteful Scotland could not capitalise and remain winless in South Africa after eight attempts.
It will be hugely frustrating for coach Gregor Townsend, whose side were on top for large parts of the contest but were let down by errors in crucial moments.
"I am a little bit gutted to be honest," Scotland captain Sione Tuipulotu said. "They (South Africa) came out really hot but we were able to battle back.
"I thought the period after halftime hurt us. We had a lot of possession in their 22 and didn't capitalise.
"I am very disappointed at the moment but also proud of the group. We played a positive brand of rugby but it wasn't good enough today."
South Africa made it a full haul of 10 points from their opening two games and will be delighted with the victory having rested so many of their regulars.
Springbok coach Rassie Erasmus took charge of a team-record 55th international fixture.
"All credit to Scotland, they came out and played unbelievably well. But I am proud of the guys, we stuck to our systems and finished well at the end," stand-in Springbok captain Pieter-Steph du Toit said.
"The system is so well prepared in this team, each player comes into the side and knows exactly what to do.
"We made some mistakes and they saw some weaknesses in our defence. We need to improve on that."
With the score level at 14-14 at halftime, South Africa lost replacement lock Ben-Jason Dixon to a yellow card for head contact at the ruck early in the second period, but Scotland did not manage a point in that period.
It took the Springboks almost 20 minutes to get into the visitors' 22 in the second half and when they did, replacement loose forward Elrigh Louw crossed to score.
That signalled a momentum shift in the match and centre Damien Willemse and replacement prop Zac Porthen crossed for tries to open up a 21-point lead.
But the visitors gave themselves hope when Josh Bayliss ran in unopposed under the posts and scrumhalf Ben White crossed shortly afterwards.
Centre Jesse Kriel sealed Scotland’s fate when he collected flyhalf Handre Pollard’s grubber kick to score a sixth try.
