Fellow Aussies Anthony Painter and Brad King shot 67 and 69, respectively, to share second place at nine-under par with American Jim Benepe, who turned in a 67.
Peter Lonard, who tied for sixth at the Greg Norman Holden International last week, carded a 70 and is four strokes off the pace with Nathan Green (67), Michael Cocking (68) and Rodger Davis (69).
Rumford, three shots back of second-round leader Adam Scott at the start of the day, stormed to the head of the pack with matching nines of four-under 32. He made a late surge with four birdies over a five-hole span to cap his round.
'I'm not really sure where that came from to tell you the truth, it's been there for the last couple of weeks,' said Rumford, who finished 46th at the Norman event. 'I just haven't been able to capitalize on anything -- if I was playing well I was just missing putts.'
Rumford made sure the onus didn't fall on his putter, as the 23- year-old flashed accurate irons to set up easy birdies down the stretch, including a three-footer at 18.
Rumford first made professional waves as an amateur when he posted a playoff victory in the Australian Tour's Players Championship at Royal Queensland in 1999. He went on to earn 2000 Rookie of the Year accolades on the strength of several strong finishes, among them a runner-up to Michael Campbell here last year.
Aaron Baddeley, who triumphed in a playoff over Sergio Garcia for the Greg Norman Holden title a week ago, snapped back into contention Saturday with a bogey-free 65 after posting back-to-back 72s over the first two days.
The 19-year-old Baddeley, a member of the Huntingdale club for the last four years, highlighted his round with two chip-ins for birdies.
'Ever though I parred three of the par-fives it was still good to get the job done,' said Baddeley, who is five shots back at minus- seven. 'I think that is the key tomorrow. If I can birdie the par- fives, I have a chance.'
Also at seven-under 209 are Peter O'Malley (69), Colin Montgomerie (70), Craig Parry (70) and the 36-hole leader Scott (72).
Click here for Full-Field scores from the Ericsson Masters!