It ensured another frustrating Rugby Championship result for the two sides for the second time in less than a month, after they fought out a 23-23 draw in Perth.
South Africa twice took the lead in a thrilling seesaw affair of a second half, while Elton Jantjies pulled a penalty wide with two minutes to play.
"It looked like nobody wants to win it", said Australia skipper Michael Hooper. "I am sure both teams extremely are frustrated".
It means the Rugby Championship returns to New Zealand for a second consecutive year and five out of six years since the tournament expanded to include Argentina.
"I've only just been back but there's certainly a very good picture for us", Beale said of the side's attack. Australia still haven't won in South Africa since 2011, and neither team has won away from home in the last eight tests between them.
Matches like this one were probably deserving of a draw but the feeling of overwhelming discontent is certainly undesirable."It's just a tiresome feeling, isn't it", Beale said.
Folau was the first try scorer of the afternoon, crossing from a pinpoint set play and similarly sharp pass from flyhalf Bernard Foley.
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The Boks did get over through prop Dreyer in the 18th, and the boots of Foley and Jantjies did the rest in the first half to give the Wallabies a 13-10 lead.
But he was left incensed when a penalty was awarded to the Springboks with less than two minutes remaining on Sunday morning (AEST), with referee Ben O'Keeffe ruling Marika Koroibete illegally used his hands in the ruck.
The tries came fast at the start of the second half.
Centre Jan Serfontein began the exchange in the 43rd minute as he dotted over after an initial burst down the wing by flanker Siya Xolisi to see the Boks go ahead for the first time.
The South Arfricans immediately hit back through Courtnall Skosan, opening up a 24-20 lead with 30 minutes to play.
Australia had a golden opportunity before Jantjies' late miss, but Tevita Kuridrani was cut down by Ross Cronje a meter from the South Africa tryline.
The 26th test match between New Zealand and Argentina will be the eighth meeting between the two sides to be held in Buenos Aires since their first-ever match in 1985, with the 49,540-capacity stadium hosting the event for the fifth time.
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