The experienced back playing at inside centre finished with 18 points from the boot, as the Springboks’ poor record in Brisbane continues.
Ill discipline once again cost the Springboks early on when Jaque Fourie was sin-binned for a cynical spear tackle on Wallabies number eight Richard Brown in the second minute.
A man down, the Springboks decided to fight fire with fire as they ran from deep with ball in hand.
But the Wallabies took the lead midway through the first half, Giteau slotting a long penalty from further poor discipline from the Springboks.
It prompted the Wallabies to take the attack to the Springboks with a number of evaded tackles and line breaks.
Two more penalties for Giteau and one from Springbok Morne Steyn left the score at 12-3.
Wallabies skipper Rocky Elsom then had a moment to forget when he broke free down the line and tried to chip Bryan Habana to set James O’Connor free, but only managed to skew into touch.
With minutes to go to the half, Giteau broke the Springbok line and passed to allow Drew Mitchell to touch down after a slight juggling act.
Giteau then landed his fourth penalty after the break and BJ Botha became the fourth Springbok to be sin-binned in three games for repeated offending at the breakdown.
The Wallabies then showed ill discipline of their own as Quade Cooper was yellow-carded for a similar offence to that of Fourie.
Fourie himself made up for his earlier indiscretion as he finished a great set play from a Ruan Pienaar tap-and-go to John Smit. Pienaar took over kicking duties but missed the resulting conversion.
He then missed a second conversion, this time from a Gurthro Steenkamp try after the prop collected the ball off Victor Matfield from a lineout and drove over the line to give the Springboks hope.
The Springboks continued to push but a try from Genia put the game to bed with just over ten minutes to go.
South Africa return home without a win while Australia move on to face the All Blacks in the first Bledisloe Cup fixture of the tournament.
Australia: A Ashley Cooper (Brumbies); J O’Connor (Western Force), R Horne (NSW Waratahs), M Giteau (Brumbies), D Mitchell (NSW Waratahs); Q Cooper (Reds), W Genia (Reds); B Robinson (NSW Waratahs), S Faingaa (Reds), S Ma’afu (Brumbies), D Mumm (NSW Waratahs), N Sharpe (Western Force), R Elsom (Brumbies, capt), D Pocock (Western Force), R Brown (Western Force)
Replacements: S Moore (Brumbies), J Slipper (Reds), R Simmons (Reds), B McCalman(Western Force), L Burgess (NSW Waratahs), B Barnes (NSW Waratahs), K Beale (NSW Waratahs)
South Africa: Z Kirchner (Bulls); G Aplon (Stormers), J Fourie (Stormers), W Olivier (Bulls), B Habana (Stormers); M Steyn (Bulls), R Pienaar (Sharks); G Steenkamp (Bulls), J Smit (Sharks, capt), BJ Botha (Ulster), D Rossouw (Bulls), V Matfield (Bulls), S Burger (Stormers), R Kankowski (Sharks), P Spies (Bulls)
Replacements: C Ralepelle (Bulls), CJ van der Linde (Cheetahs), F van der Merwe (Bulls), D Potgieter (Bulls), F Hougaard (Bulls), B James (Bath), J de Jongh (Stormers)
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