The Blackpool left-back's well struck goal in the 53rd minute proved the difference as the Socceroos remained unbeaten in five encounters with the higher-ranked South Americans.
It was Australia's final home international ahead of the Asian Cup with a match against Egypt likely in Cairo next month. Australia also remained unbeaten in three games under their new German head coach Holger Osieck, who took over from Dutchman Pim Verbeek after this year's FIFA World Cup in South Africa.
"When we get our stuff together we are defensively well organised and set up, and if we play very courageously like we did today then I am confident that the Asian Cup will be a very good tournament for us," Osieck said.
Osieck played star Everton midfielder Tim Cahill for 76 minutes and brought off Galatasaray's Harry Kewell with a few minutes left. Goalkeeper Mark Schwarzer, who deputised for injured skipper Lucas Neill, kept a clean sheet and was only called on to make four saves during the match.
The match got a bit messy in the second half and twice Japanese referee Yuichi Nishimura pulled out the yellow card for Paraguayans Dario Veron and Claudio Rodriguez. Spain-based striker Nelson Valdez had Paraguay's best and only chance of the opening half when his shot on the turn was well taken by Schwarzer after 13 minutes.
Australia took time to find their rhythm but forced Paraguay goalkeeper Diego Barreto to make two saves in as many minutes midway through the opening half. Unmarked Cahill launched a free header off a Luke Wilkshire free kick which Barreto saved and the Paraguayan keeper was again at full stretch to block a fierce long-range volley from midfielder Jason Culina moments later.
Australia appealed for a penalty in stoppage time when Victor Caceres appeared to bring down Mile Jedinak while jostling for a Wilkshire free kick. Barreto made another diving save to deny Richard Garcia just minutes after the interval.
Carney put the Australians a goal up eight minutes after the break with a stinging volley which beat Barreto at the near post. The Australians had more of the play and it was only in the final 15 minutes that Paraguay came more into it with Carlos Bonet and substitute Federico Santander looking dangerous.
The loss continued Paraguay's mixed results on their Asian tour, after they lost 1-0 to Japan in Yokohama and drew 1-1 with China PR in Beijing. Australia have yet to lose in their five encounters with Paraguay, all of them in Australia.
Paraguay have a match against fellow FIFA World Cup team New Zealand in Wellington on 12 October.