Peter Lonard had five birdies and an eagle for a 15-point total, one point ahead of Craig Parry, who finished tied for second at this event last year.
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.
Fowler played the back nine first at New South Wales Golf Club and had three birdies over his first nine holes to pick up six points under perfect conditions. Fowler continued his fine play on the front half with birdies at the first and third holes.
The Australian birdied the par-5 fifth for the first of four consecutive birdies to surge into the lead. Fowler had 18 points but faltered with a bogey at the ninth, his last, to finish with a slim margin after Round 1.
'My game's coming together,' said Fowler. 'I work out six times a week in the gym and I've started the year with a higher base. I feel rejuvenated, I'm feeling good. I feel like a rookie.'
The 43-year-old, who achieved his only victory on the European Tour at the 1993 BMW International Open, has fought hard to maintain his playing privileges, including several trips to qualifying school over the past few years.
'It's hard losing your card and being told that you're not good enough, so I've had to dig deep,' said Fowler. 'I really had to think hard and get help from good people. And it's paid off.'
Appleby had a bogey-free round and managed eight birdies to finish one point off the pace.
'Three more rounds like that and I'd have a winning chance,' said Appleby. 'The course is just awesome. Linksy style and we just don't have enough of these layouts.'
Tobias Dier, Matthew Blackey and Steve Collins finished tied for fifth with 12 points each. Stephen Scahill, David Howell, Stephen Leaney, Robert Karlsson and Steven Conran each had 11 points to finish in a tie for eighth.
David Drysdale, Jean-Francois Remesy, Steve Webster, Terry Price, Brad Kennedy, Nick O'Hern, Henrik Bjornstad, David Carter, Marcus Cain, Peter Senior and Michael Pearson were knotted at 10 points.
This event is co-sanctioned by the European and Australasian Tours.