Robert Karlsson of Sweden finished alone in third with 31 points. He was followed by Nick Dougherty, who collected 17 third-round points, and Nick O'Hern with 30 points.
The tournament uses the modified stableford scoring system which promotes aggressive play. The scoring awards eight points for a double-eagle, five points for an eagle, two for a birdie and none for a par. One point is deducted for a bogey and three points are taken away for a double-bogey or worse.
Casey struggled early at New South Wales Golf Club with a bogey at the opening hole but recovered in brilliant fashion. He picked up back-to-back birdies starting at the par-4 third and eagled the par-5 fifth.
At the seventh, Casey made the first of three consecutive birdies to make the turn with 32 points.
'I think this format suits me,' said Casey. 'I wish every week was like this.'
The 25-year-old had four birdies and one bogey on the back nine to give him a six-point lead with one round to play.
'I'm going to go out there and just try and attack the golf course again,' said Casey, who got his breakthrough win on the European Tour at the 2001 Scottish PGA Championship. 'Try and make as many birdies and give myself as many opportunities as I can.'
Appleby, who played alongside Casey, birdied the fourth and the sixth but found trouble with a double-bogey at the par-4 seventh. He bounced back with a birdie at the eighth and torched the back nine with six birdies to move into second place.
'We played pretty good. I was certainly playing second fiddle to Paul, he played fantastic all day, he just blitzed that front nine,' said Appleby. 'He was lapping me, dancing around me, I was almost watching and making an odd swipe here and there.'
Peter Fowler, who held the lead after the first round, finished tied for sixth with 29 points along with Scott Hend. Peter Senior was alone in eighth with 28 points.
Gregory Havret, Ignacio Garrido, David Howell and Terry Price were tied for ninth with 26 points. Jamie Donaldson, Marcus Cain, Richard Lee and Nathan Green followed with 25 points each.
This event is co-sanctioned by the European and Australasian Tours.