Joe Root’s team backed the hosts into a corner over the first three days – 465 runs behind and with six entire sessions in front of them – then finished the job by dismissing them for 274.
The Proteas showed some fight, notably in the form of Rassie van der Dussen’s 98, but England’s pace attack was too strong, Mark Wood taking four more wickets for a match haul of 9-100.
Ben Stokes was also key, breaking open the two biggest stands of the day by dismissing Dean Elgar at the end of the morning session and captain Faf du Plessis just before tea. Du Plessis was earlier seen nudging Jos Buttler with his shoulder and could find the pain of defeat exacerbated by disciplinary action.
Victory at Johannesburg’s vaunted ‘Bullring’ completed a famous hat-trick of wins behind enemy lines, following the day five drama in Cape Town and the domination of Port Elizabeth.
It is just the third time since 1979 that England have won three in a row on the road, a feat that escaped Andrew Strauss and Alastair Cook entirely, but which Root has now achieved twice.
Pieter Malan and Elgar set the right tone for their side, blunting the new ball as they put on a chanceless 39 in the first hour. They will have been satisfied with their work as they headed to the drinks break but as soon as play resumed Malan was out, driving loosely at Chris Woakes.
Van der Dussen came to the crease on a pair in his first Test as a No 3 and was given lbw to Woakes on nought, escaping after a successful call for DRS. Getting off the mark with a pull for four, he went on to add 50 with Elgar and dealt mercilessly with three overs of Root’s off-spin.
Lunch was hovering into view when Stokes intervened in his last over before the break, pounding one into the pitch and towards Elgar’s helmet. The batsmen flailed in self-defence and popped a return catch back to Stokes.
Van der Dussen and Du Plessis held court for the next two hours and 20 minutes, putting plenty of hard labour into the English attack.
Van der Dussen was largely enjoying himself, moving to his third half-century of the series, then past his previous best of 68 in calm fashion. When Joe Denly tried his luck for three overs, his rag-tag leg-breaks were summarily dispatched.
Du Plessis’s stay was more of a scrap, at one stage almost literally. He was beaten a couple of times before getting off the mark from his 18th ball, rapped on the glove when Woakes found some joy from a crack outside off and almost played on with 10 to his name.
Wood was next to try his resolve, forcing Du Plessis back with a fierce bouncer and almost causing him to fall into his own stumps. The captain’s adrenaline was hardly any surprise but when he pushed his shoulder against Buttler it was a step too far.
There was some mitigation, an ongoing verbal spat with Broad and a loose Curran throw that thumped into his pads, but any physical contact is liable to be punished by the match referee.
The only blow that really counted was the one about to be inflicted by Stokes, who charged in again and bowled Du Plessis for 35 as the ball kept low and skimmed off the toe end.
After repelling England for so long the spell was broken and Van der Dussen was gone in the next over. He had batted brilliantly and deserved his side’s first ton of the series, but when Wood attacked from round the wicket he popped a catch to short cover.
Temba Bavuma and Quinton de Kock peppered the boundaries immediately after tea but the writing was on the wall.
Broad returned to the attack and struck twice in his first two overs, Bavuma arching his back dramatically as he gloved behind and Dwaine Pretorius top-edging to fine-leg.
Vernon Philander came out to bat with a torn hamstring but his final act before retirement was a short one, strangled down leg by Wood.
Beuran Hendricks was run out and the series was settled in England’s favour when Buttler and Wood combined for Anrich Nortje’s wicket.