Dom Sibley delighted in the aftermath of a maiden Test century, helping England fasten their grip on the Cape Town match.
South Africa opener Dean Elgar took the blame for his first dismissal at Newlands, but he was not happy with Ultra-Edge the second time.
An impressive early stand from Pieter Malan checked England's progress after Dom Sibley's first Test century teed up victory.
Pat Brown has suffered a lower back stress fracture and will miss England's white-ball tour of South Africa in February.
After a quiet return at Centurion last time out, James Anderson was back to his best to help England's cause in the second Test.
England seized control of the second Test with a composed performance on Sunday, Dom Sibley the star of the show in Cape Town.
The key wicket of day two at Cape Town was a "brainfart", said apologetic South Africa opener Dean Elgar.
England had the better of day two in the second Test against South Africa, with Ben Stokes, James Anderson and Stuart Broad stepping up.
England's key men, led by James Anderson, raised their game just as South Africa looked to be taking charge of the second Test in Cape Town.
Dwaine Pretorius was more than happy after South Africa took nine wickets on the first day of the second Test against England.