The tourists crashed through the brittle South African batting lineup twice on the fourth day in Port Elizabeth. England first took four wickets for one run in less than five overs at the very start to bowl the home team out for 209 in its first innings after the hosts resumed the day on 208-6.
Then, England captain Joe Root led with a career-best four wickets with his part-time offspin as South Africa, following on, slumped again to 102-6 at stumps in its second innings.
Root's young England team, half of which is under 25, was on the way to a landmark win. England is expected to see out victory on the final day on Monday and take a 2-1 series lead with one test to play.
The South Africans were still 188 runs from England's first-innings score of 499-9 declared and faced a psychologically scarring defeat ahead of that series finale in Johannesburg.
England has a chance to go to Joburg off the back of its heaviest defeat of South Africa in more than 100 years.
The only obstacle appeared to be the rain, which stopped play for more than three hours on Sunday and might return to frustrate England on the final day. Three of the first four days have been rain affected.
"Don't (talk about rain)," said England fast bowler Mark Wood. "No. I'm concerned. I thought Africa was the sunniest place in the world. I am a little bit worried.
"(But) If we have the same attitude tomorrow ... then I think we'll be in a good place."
Sunday's rain delay certainly didn't dampen England's fire.
England's fast bowlers ripped through South Africa first. Stuart Broad took three of the four wickets in that devastating early England spell to wipe out South Africa's first innings.
That gave England a 290-run first-innings lead and Root made South Africa follow on.
Broad took his three wickets in 16 balls. Sam Curran had the other one, and three of the four were convincingly bowled as South African stumps flew in all directions.
Broad bowled Vernon Philander (27) in the first over of the day with a ball that smashed into Philander's off and middle stumps.
Curran did the same to Quinton de Kock, who was 63 not out overnight but had his middle stump uprooted in the second over of the day. Neither of the two batsmen added a run to their overnight scores.
Broad bowled tailender Keshav Maharaj for a duck in the next over. Again, the ball clattered into Maharaj's stumps — this time off a bottom edge — and England was utterly rampant.
Broad had his third wicket in three overs when Kagiso Rabada was last man out and England finished the job in the first 28 balls of the day for a resounding statement.
South Africa had shown a hint of resistance on the third day through de Kock and Philander's half-century partnership. That was ruthlessly swept aside the following morning.
Broad finished with 3-30 after England's blitz. Spinner Dom Bess took 5-51 and England didn't even need him to finish off South Africa's first innings.
The rain then did what no South African could and held up England for more than three hours.
The tourists picked up where they left off in the afternoon, though, when quick bowler Wood ruined opener Dean Elgar's stumps to start the second-innings onslaught.
"Like any fast bowler I want to see a stump go flying and that was a great feeling," Wood said.
South Africa slipped further to 44-3 at tea and was in danger of losing by an innings with more than a day left.
South Africa captain Faf du Plessis fought hard with his 36 but was out to his England counterpart Root with a clear bat-pad catch that he strangely reviewed. South Africa appeared all but done with just the bowlers left to try and save the test with the bat on the last day. Root has 4-31 off 19 overs.
England, after going 1-0 down at the start of the series, is on course to turn it right around.
South Africa was slumping and has its best bowler, Kagiso Rabada, banned for the final test, an inexperienced batting lineup and a new head coach under grinding pressure. Add to that unsettling rumors circulating that captain du Plessis is about to retire from test cricket.
"It's easy to point fingers at this and that and the system," said head coach Mark Boucher, who was appointed less than two weeks ahead of this series. "But for me there's no excuses. I need to find some way to get it right in a very short period of time."