Els, the fourth-ranked golfer in the world, carded a 2-over 73 in difficult conditions at The Grand Golf Club, where only eight of the 60 players in the field broke par Saturday and just five were under par after 54 holes.
'My start didn't help,' said Els, who had two of his four bogeys on the front nine. 'I didn't quite hit my iron shots the way I wanted to, and then when you start missing you've got to get it up and down and I felt like I had to do that all day.'
The two-time U.S. Open champion hit only half the fairways and 12 of 18 greens in round three. He also stroked 32 putts, six more than he needed over each of the first two days.
Els did finish on an up note, however, sinking a 10-foot birdie putt at the 17th hole before parring the last to finish alone in third place.
Geoff Ogilvy (74) was solo fourth at 3-under-par while Rod Pampling (75) finished alone in fifth place at minus-two.
Appleby managed to negotiate the tricky winds in bogey-free fashion, posting birdies at the fourth, 10th, 13th and 17th to earn a share of the top spot.
'You can get hit pretty hard here, I was pretty nervous all day,' said Appleby, who missed the cut at last week's Australian PGA Championship. 'To win here would be a great way to end the year, but the year's not ended yet. I've got one more round to go.'
Laycock, the overnight leader at 7-under, couldn't budge off that number after an even-par 71. He did push three shots clear of the field with birdies on the first and fourth holes but fell back to the pack after bogeying the ninth and 11th.
'It's one of the hardest rounds I've played,' he said.
Ogilvy was just one shot off Laycock's pace through two rounds but experienced a nightmare start Saturday with three bogeys, a double and a triple after 10 holes, dropping him to 2-over-par.
He battled back by picking up five strokes over the final seven holes, closing with a 30-foot eagle putt at the 17th and a 20-footer for birdie at No. 18.
Pampling, also one back at the start, was able to hold steady with 10 straight pars but suffered four bogeys in the way in.
Denmark's Thomas Bjorn rebounded from an opening 76 with rounds of 67-70 on Friday and Saturday. He was tied for sixth place at even-par 213 with Brett Rumford, Peter Lonard and amateur James Nitties.
Greg Chalmers, the winner of the 1998 Australian Open, rounded out the top 10 with Adam Scott and New Zealand's Richard Lee at 1-over par.
Full-Field Scores From the Holden Australian Open