A try from Cornal Hendricks gave the Springboks an early lead, before a second from Branco du Preez stretched their advantage.
Seabelo Senatla scored a third try for his side, taking his tally to eight in the tournament, before Mark Bennett touched down to make it 21-7 at half-time.
After the restart, Lee Jones went over for his sixth try of the competition before a second try from Senatla and another from Cecil Afrika put the Boks out of sight.
The Scots went on to face England in the semi-final of the Plate but went down 15-12, with tries from Mark Bennett and Lee Jones.