Bavuma's 179 across the first three days at St George's Park could well prove series-defining, after the Proteas captain led them from 6-110 to 9(dec)-425.
His innings means South Africa should at least go to Cape Town next week with a chance to draw the series, with victory in Gqeberha also still not entirely out of the question.
After coming to the wicket with Scott Boland on a hat-trick and South Africa 2-20, the Proteas captain showed poise and patience before taking charge on day three.
But most impressive was the fact it came just a week after he admitted he had been unhappy with his own batting in Durban, scoring three and one in defeat.
That prompted multiple long sessions in the St George's Park nets, and again mid-innings back indoors after day one when rain stopped play.
"I've been struggling for the rhythm since the start of the season, throughout the ODI series, even building up to the first Test," Bavuma said.
"Being in the nets was always trying to find that feeling. I don't know how else I could explain it.
"Not so much from a technical point of view, but just a feeling that I could hold on to and be able to compete out there in the middle.
"I guess throughout the innings I kind of battled through it, found some fluency, and obviously found a game plan as well, which I stuck to."
While Marco Jansen thrashed 85 at the other end in a 132-run seventh-wicket stand and Simon Harmer hit 82 in a 183-run eighth-wicket partnership, Bavuma's knock was one of patience.
When he walked to the wicket on Sunday it looked like every ball could have a batter's name on it.
But the 36-year-old left well, took 226 balls to bring up his century and meticulously batted the Proteas back into the game and then into command.
Since becoming captain in 2023, Bavuma's record stands at 11 wins, one draw and one loss in Durban last week.
This was his fourth century in that time, averaging 54.36 as leader. And it's hard to argue against it being his most important.
"I'm happy that I was able to get one against Australia in Test cricket. So I think there's that firstly," Bavuma said.
"The one thing just from a personal point of view, is the fact that I was able to get the team out of a tough situation.
"But then from a personal point of view, to go into the day, to get a big hundred, that's always been something that's been a thorn in my batting career.
"So it was nice to mentally get over that."
17°C