Centre Jesse Kriel and hooker Malcolm Marx crossed for the Springboks, who dominated the breakdown and set piece but were unable to convert late pressure into a score that would have given them a sixth successive win.
Livewire centre Kurtley Beale and hooker Tatafu Polota-Nau scored tries for the Wallabies, who showed plenty of attacking endeavour but remain winless in the competition after back-to-back losses to the All Blacks.
"That was a proper test match. That's what they're all about," said Springboks captain Eben Etzebeth after only the second draw between the two countries in 84 meetings.
"Awesome effort in the second half. We had to work on a couple of things and we almost pulled it off. You always want to win, but we will take the draw."
Western Force forward Polota-Nau's try was particularly popular with a crowd of 17,500 studded with fans wearing the blue shirt of the recently axed local Super Rugby franchise.
There were no major protests at the Australian Rugby Union's decision, however, and the Wallabies received the whole-hearted backing of the locals.
"Missed opportunity there," said Australia captain Michael Hooper. "The set piece was tough for us to build pressure. Re-start wasn't up to scratch again but plenty to like there as well."
A sprinkling of rain just before kickoff did nothing to dull the attacking intent of either side even if the result in terms of points was initially limited to an exchange of penalties.
The Wallabies had been making plenty of breaks but were being outmuscled at the breakdown and it was from one of a string of turnovers that the Springboks scored the first try in the 26th minute.
Scrumhalf Ross Cronje quickly flipped the ball out to Jesse Kriel, who chased his own kick ahead and touched down after winger Raymond Rhule and Hooper had taken each other out.
Australia had been focusing on the restart in training and replied directly from the ensuing kickoff with Beale picking up a poor pass that looked to have stalled the attack before cutting back to slice through the blindside defence.
Bernard Foley slotted his second penalty on the stroke of halftime to give the hosts a 13-10 advantage and the converted pushover try from Polota-Nau seven minutes into the second half extended the lead to 10 points.
The Springboks struck back when Elton Jantjies kicked his second penalty to reduce the deficit before the visitors got their own rolling maul going from an attacking lineout to send Marx over to level up the scores with 20 minutes to play.
A dominant scrum in the 66th minute gave flyhalf Jantjies the simplest of chances to put South Africa up 23-20 but Foley responded immediately with a long-range effort to set up a tense last 10 minutes.
South Africa had the best chance of grabbing the win, going through phase after phase inside the Australia half as time ran out but Jantjies fluffed his drop goal attempt when the ball finally came back to him.
The Springboks take on the All Blacks in Auckland next week, while Australia host Argentina in Canberra.