Neither side could score in a lacklustre first half, as Ben McCalman had a try ruled out for the hosts.
France also missed two penalties in a scrappy opening before Bernard Foley finally opened the scoring in the 53rd minute.
Foley's penalty was added to by Nic White " who kicked just one of his four attempts " 15 minutes before the end.
France were then reduced to 14 men when reserve forward Bernard Le Roux was yellow carded for a breakdown infringement in the 70th minute.
They still had a chance to win, though, and a sustained attack after the siren gave them an opportunity to steal victory.
But a committed Wallabies defence held on for a low-scoring win in a match that featured too much kicking and countless scrum re-sets.
Australia have now won their last six Test matches and take a 2-0 lead into the third and final clash of the series in Sydney next week.
It was quickly evident the 10 changes France coach Philippe Saint-Andre made to his starting side would result in a far more competitive performance than what was offered in last week's 50-23 drubbing in Brisbane.
As expected, France flooded the breakdown early and dominated territory and possession as a result.
France full-back Brice Dulin just missed a 51-metre penalty attempt in the 17th minute before McCalman's try was disallowed when it was ruled that Matt Toomua took out Dulin attempting to field the ball in his own in-goal area.
Morgan Parra missed a long-range penalty goal in the 37th minute before Yannick Nyanga blew France's only legitimate chance to score a try moments later.
The imposing flanker charged down a Toomua kick and should have scored but knocked on trying to pick the ball up to leave scores locked at 0-0 at the break.
The drought continued at the resumption as White missed two long-range penalty goals in the opening four minutes.
His second miss hit the post and Adam Ashley-Cooper grabbed the rebound but the Wallabies squandered that attacking opportunity to let the visitors off the hook.
Foley finally broke the deadlock with a penalty goal that was received by sarcastic cheers from the crowd.
The Wallabies turned down another penalty goal in the 63rd minute and kicked for the corner before White finally found his range, slotting from directly in front to give Australia what proved to be a match-winning lead.