The Springboks, who also scored tries through prop Thomas du Toit and No.8 Jasper Wiese, made 11 changes for Sunday's match and looked disjointed, not helped by 21 handling errors that broke their momentum.
It was a ninth successive loss to South Africa for the Scots, but there will be aspects of their performance they will be pleased with, though they failed to take their chances in the visitors' 22, with all their points coming from the boot of flyhalf Finn Russell.
South Africa next travel to Twickenham to play England on Saturday, while Scotland host Portugal on the same day.
"It was a tough Test match, Scotland are always difficult to play against and they gave us problems in the first half especially. The scoreline flatters us a bit, it was closer than that," Springbok captain Eben Etzebeth said.
It is the second meeting in a row that South Africa have kept Scotland from crossing their try-line having also kept them out at the Rugby World Cup last year.
South Africa dominated the early possession and Handre Pollard's cross-kick was perfect for Mapimpi to gather and score in the corner.
Scotland were reduced to 14 when lock Scott Cummings was penalised on TMO review for a croc-roll at the ruck on Springbok counterpart Franco Mostert that met the threshold for dangerous play.
He initially received a yellow card, but on bunker review it was upgraded to a 20-minute red card which ended his participation in the game, though he was replaced later on by Max Williamson.
Russell added two penalties in the first half as Scotland looked to have managed their numerical disadvantage superbly with some ferocious tackling to apply pressure on the visitors.
But as the seconds ticked down to them being back to their full complement, the visitors scored a second try from a messy attacking line-out as lock Mostert missed the throw and the ball fell kindly for prop Du Toit to gather and have a clean run to the line.
The Springboks added a third when Scotland halfback Ben White took too long to clear from the base of the ruck and from the resultant scrum, fullback Willie le Roux's kick was collected by Mapimpi to coast in.
The Springboks, who selected seven forwards on the bench, brought on six of them after 45 minutes, but Scotland fed off the visitors' numerous errors to stay in the contest.
Mapimpi received a yellow just before the hour-mark for cynical play and Russell closed the gap to five with a penalty.
But South Africa are masters at closing out games and took control again in the final 20 minutes as they won several scrum penalties before Wiese crossed for a try with the final play of the game.
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