Ninyette hit seven birdies to offset two bogeys for a five-under-par 67 and took his three-day total to eight-under at the $2 million event, which is co-sanctioned by the European Tour and PGA Tour of Australasia.
Rumford was on the verge of a new course record and drawing level with Ninyette but missed a three-foot putt on his final hole for his lone bogey of the day and had to share second spot with Dane JB Hansen and South Korean Jin Jeong on seven-under.
"The greens were receptive with the wedges, and my wedge game was great today," Rumford told reporters after his 65. "It was a mixed bag of everything that was working well.
"It's disappointing to have three putted the last, no doubt about it, but obviously my mind set, playing so well, was too aggressive on the last."
The 36-year-old was excited to play in front of his home crowd and a victory on Sunday will be the icing on his cake.
"It's great to play in front of the local galleries. It was nice to get out there and just to play some nice golf," he said.
"The crowds were starting to increase as my round progressed and it was giving me an indication of how I was going.
"It would be massive to win on home soil."
For Ninyette, who mostly plays on the PGA Tour of Australasia, a win will provide a ticket to play in Europe next season.
"I've been playing well the last few days," he said. "It was good to hole a few putts and get myself into contention.
"Obviously being able to play in Europe next year; that would be one of the bigger things. Just getting to travel a lot more.
"It would be a whole new experience, getting out there and playing over there would be unreal to see how the world's best do it. I've only played these sort of tournaments in Australia."
Other Australians celebrating on Saturday were David McKenzie and Rohan Blizard who both recorded holes-in-one during their third round.
Overnight leader Peter Hedblom, who needs a victory to retain his Tour card, was four shots behind the leader after a disappointing three-over 75.
American Ryder Cup player Dustin Johnson trailed the leaders by 10 shots while his compatriot and defending champion Bo Van Pelt was four strokes adrift.