The game, played in dank conditions and under grey skies in southwest London, turned in the final 10 minutes of the first half after Eben Etzebeth - South Africa's man mountain at lock - walked off the field groggily in the 30th following a clash of heads with England No. 8 Billy Vunipola.
The Springboks were 9-7 ahead at that point and their physicality was causing England to make panicky decisions and handling errors in the wet conditions. By halftime, England scored 13 unanswered points and was on its way to the latest win of the Jones era.
Pat Lambie's two penalties and left-footed dropped goal gave South Africa a foothold after 20 minutes, during which England conceded six penalties but scored an impressive try - given the conditions - when winger May slid in at the left corner after the ball was worked across the line.
Losing Etzebeth - the Springboks' most experienced player and vital cog in the pack - was a huge blow to the visitors. England won a penalty at the very next scrum after the Springboks collapsed it, and Farrell kicked the three points to give his team a lead that was never relinquished.
Then came Lawes' first international try, after Springbok wing Ruan Combrinck fumbled the ball backward as he was tackled. England fullback Mike Brown hacked it forward and was about to collect when Lambie got his hand to the ball. Lawes was alert to the loose ball, which squirmed over the line, and dived onto it for a try that needed the say-so of the TMO.
A booming penalty from the halfway line by debutant Elliot Daly with the last touch of the first half put England 11 points clear, and the South Africans were further demoralized when scrumhalf Ben Youngs dummied his way through the defensive line and popped a pass up for Ford to run clear and dive over.
The match became one-sided. Lambie kicked the restart straight into touch, Farrell booted another penalty, and England was suddenly 30-9 up.
Goosen sprinted clear for a try in the 59th from Warren Whiteley's inside pass to reduce the deficit and Le Roux's try in the 79th ensured the Springboks didn't succumb to a second-worst loss to the English.
Between those Springbok scores, Farrell made it 19 points for the match by scoring England's fourth try after Youngs produced another dummy - again deceiving Pieter-Steph du Toit - to break the line.
England is three more victories away from matching its longest winning streak of 14 games.
- AAP