Steyn will be out for at least six months after hurting his shoulder on the second day in Perth, but he was barely missed as Rabada, 21, stepped up with a five-wicket haul in the second innings.
Rabada takes five as South Africa seal victory
The right-armer claimed 5-92, his fourth five-wicket haul in his short career, to guide South Africa to victory by 177 runs, bowling more deliveries than in any of his eight previous Tests.
"It is not nice losing the best bowler in the world and being down to two seamers, but we still had to believe," Rabada said. "I don't see myself as leading the attack, I know that I have a job to do and I just try to do my job.
"I've got a responsibility to make sure I produce the goods for the country. It's a passion and you do it for your team-mates and the people back home, because no one wants to lose and you have to try to do everything you can to win."
Rabada fires as South Africa close on opening Test win
South African captain Faf du Plessis praised Rabada and said he shown all the signs of being a "champion bowler".
"I am incredibly proud of him and I have a lot of respect for anyone who puts their hands up and does the hard yards," du Plessis said. "He wanted the ball and that is the sign of a champion bowler who wants to be in the fight all the time."
Rabada was particularly pleased with his over to Adam Voges on the fourth day, when he bowled a couple of superb deliveries and then had the veteran batsman caught behind for one.
"I enjoyed that over," he said. "A new batter coming in, the ball was reversing nicely and I was feeling my best rhythm.
"Sometimes you get a wicket exactly how you want and it was one of those times."
Rabada also said the heavy workload didn't concern him, as he had bowled similar amounts playing for Kent.
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