Sweden's Richard Johnson collected six birdies, an eagle and a bogey en route to the day's best haul of 16 points. He moved into a share of third place at 35 points with Scotland's Stephen Gallacher, who earned 13 points on Saturday.
The modified Stableford scoring system, which is being used in a European Tour event for the first time since 1991, awards five points for an eagle, two for a birdie and none for a par. One point is deducted for a bogey and three are taken away for a double-bogey or worse.
Stolz, who led South African Trevor Immelman by one when the
weather-suspended second round was completed Saturday morning, made five birdies in the first 14 holes at the Lakes Golf Club to top the leaderboard with 40 points late in the day.
He bogeyed the par-5 17th, however, after hitting his second shot with a 3-wood into the water.
'I played quite nice today hitting some good shots,' said Stolz, whose wife, professional golfer Cathy Nielson, is carrying his bag this week. 'For me, I'm always happy when I'm in pretty good control of my game and the rhythm is there.'
Parry suffered four bogeys on the front nine, including three in a row from the fifth hole. He battled back on the inward side with five birdies in six holes before dropping a point with a bogey at the par-3 18th.
'I could feel the event slipping away a bit there on the front nine,' said Parry, who also finished with nine points Saturday. 'But I just thought that I wasn't playing strokeplay, so I just went on the attack and started shooting some low scores, which was good.'
Parry, nicknamed 'Popeye' because of his big forearms, vaulted to the top of the Australasian Tour's Order of Merit on the strength of his win in last month's New Zealand Open.
Scott Laycock was alone in fifth place with 34 points followed by fellow Aussie Peter O'Malley, who finished the day with 33 points after pulling in 15 in round three.
Also with 15 points Saturday was Nick O'Hern. He finished with 32 points alongside Immelman, who could muster only three points on four birdies and five bogeys.
Greg Turner, David Lynn, Carlos Rodiles and first-round leader Jonathan Lomas rounded out the top-10 with 30 points.
Full-field scores from the ANZ Championship