Australia dominated possession but struggled to create genuine chances to test the Paraguay rearguard over the 90 minutes.
Carney's winner came just under ten minutes inside the second-half as he reacted first to a scrambled knockdown inside the visitors' area to thump home a winner.
Sydney's soccer fans failed to show up on the night, with barely 25,000 attending. The Sydney soccer public were upstaged by Melbourne's sports fans who outdrew the international for the previous evening's Melbourne derby between Melbourne Heart and Melbourne Victory.
Positive for Australia and Galatasaray was Harry Kewell's solid performance.
"It was a good test," Kewell said at the final whistle. "Paraguay were tough opponents and it was a good hit out for us.
"I thought we were positive and deserved the win."