Rabada was on the losing side despite taking a maiden five-wicket haul in Johannesburg but he put the Proteas well on course for a consolation victory with career-best figures of seven for 112.
With Dale Steyn and Vernon Philander injured, Rabada has been thrust to the fore in this series and he bowled with sustained pace and penetration that belied his inexperience.
England were dismissed for 342 and were 175 behind by stumps as South Africa moved to 42 for one in the second innings.
On a pitch that has shown frequent examples of irregular bounce, notably shooters around off stump from the Pavilion End, the size of the hosts’ advantage may already be decisive.
England will not relish any kind of fourth innings chase but with Kyle Abbott nursing a hamstring injury, South Africa may also find themselves short of options at the business end of the match.
Indeed, it seems as though Rabada will again have to shoulder a sizeable burden alongside Morne Morkel.
The day began with Alastair Cook and Joe Root together at 138 for two, on 67no and 31no respectively.
The wheel turned just before drinks when Morkel came round the wicket to Cook, forced him to play and kissed the outside edge.
Cook departed for 76 and opened the door.
It was Rabada who burst through it, returning for a fast, accurate second spell that brought the wickets of Root (76), James Taylor (14) and Jonny Bairstow (nought).
Rain ensured a false start to the afternoon session but when play resumed, Ben Stokes found himself in centre stage.
He raced to 33, muscling the older, softer ball to the boundary five times and over the top – off Dane Piedt – once.
Kagiso Babada (RSA), youngest fast bowler to get 7 wickets in 1 innings #Rabada WINNER ✊?✊????? pic.twitter.com/JLB4qcDpB2
— RSA Min of Sport (@MbalulaFikile) January 24, 2016
But Rabada needed just two deliveries with the new ball to end his fun, shading one towards the cordon and providing Hashim Amla with a regulation slip catch.
Chris Woakes put a dropped chance behind him and set about adding 43 alongside fellow Birmingham boy Moeen.
Moeen batted intelligently with Woakes and then Broad and Anderson, coaxing stands worth 47 out of the tail-end pair and, with 61, making his highest score in 15 innings.
Broad became the seventh and last of Rabada’s victims when he picked out deep midwicket and Moeen completed the innings by chipping Piedt to cover.
Taking to the field 133 in arrears, England at least made an early breakthrough as Anderson needed just eight balls to account for Elgar.
England needed more of the same and quickly but the best they managed was a sore thumb for Hashim Amla, who was hit by the threatening Stokes before bad light intervened.
