The Wallabies have now won only once in five matches, beating the Springboks in the reverse fixture, and the scoreline could well have been harsher on Cheika and his side in Port Elizabeth.
Australia was humbled at home by Argentina last time out, and only the hosts' profligacy at one end and sloppiness at the other prevented a big margin for the Springboks, who shocked world champion New Zealand in their previous match.
Handre Pollard's trusty boot ultimately proved the difference after the sides traded two first-half tries, as South Africa's fortunes under Rassie Erasmus continue to improve in contrast with Cheika's desperate Wallabies slump.
A second win in seven meetings with Australia was thoroughly deserved and the Boks have now earned back-to-back Rugby Championship wins against different opponents for the first time since 2014, providing another boost ahead of a crunch clash with the All Blacks.
Australia's dismal campaign continued from the off as Aphiwe Dyantyi crossed inside a minute, punishing a loose Kurtley Beale pass with a simple opening try.
The Springboks attacked at pace to press for further early opportunities and Faf de Klerk was freed by Pollard's fine work to streak clear for a second score.
But a quick-fire Wallabies double came against the run of play. Will Genia first forged an opening for Reece Hodge to lunge over in the corner, before creator turned scorer and touched down on the opposite flank.
The influential Pollard ensured South Africa remained well on top heading into half-time, however, with two penalties shortly before the interval.
Another expertly dispatched kick followed the restart, although the Boks failed to capitalise on a series of speedy breaks, their passing too often muddled at key moments.
Their wastefulness invited a spell of Australia dominance but it too lacked the requisite cutting edge in attack, even with Dyantyi heading to the sin bin.
The Wallabies were unable to narrow the advantage at all and remain adrift at the bottom of the Rugby Championship standings, with just a trip to Argentina remaining as they no doubt plan to quickly forget about this campaign.