Rabada removed Joe Root for 76, and then James Taylor and Jonny Bairstow — all in the 15 minutes before lunch — to put South Africa in control of a series ender it is desperate to win to regain some lost pride.
England has already clinched the four-match series with a 2-0 lead with one game remaining.
England lost four wickets in total in the morning session on the third day at SuperSport Park, starting with captain Alastair Cook, also for 76, when he edged behind off Morne Morkel.
That broke a 99-run partnership between Cook and Root, and Rabada followed up by knocking over three more England wickets to go with his two from the second day.
Rabada raced to his five-wicket haul when he had Root out to a thin edge behind, and then got Taylor and Bairstow in his next over, the last before lunch.
It gave the young speedster five-wicket hauls in back-to-back tests following his 5-78 in England's win in the third test in Johannesburg. His 5-76 in this game was punctuated by the last spell before the break, when he took three wickets for three runs in four overs.
Cook, who needed 117 to become the first Englishman to 10,000 test runs, never got going in overcast conditions that hung around for the entire morning session in Centurion. He added just nine runs to his overnight score before prodding at a Morkel delivery and edging to wicketkeeper Quinton de Kock.
Root showed more enterprise, hitting three fours in an over early on when he was also missed by JP Duminy at gully. Root registered his third half-century of the series, to go with his hundred in Johannesburg.
He had also survived via an umpire decision review after being given out to a gloved catch behind off spinner Dane Piedt. But he fell in the third over before lunch when Rabada produced just enough outswing to find an edge to De Kock.
Rabada steamed in next over, forcing Taylor out caught behind trying to hook, and getting rid of Bairstow for a duck caught behind again off the glove.
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