'That that was hard work is an understatement,' said Appleby, who started the day tied atop the leaderboard with Laycock at 7-under. 'I knew Scotty was going to push me all the way, he was swinging it so smooth, and we were really fighting it hard.'
Still knotted with Appleby after seven holes, Laycock failed to get up and down out of a bunker at the par-3 eighth and fell one shot off the pace.
After the pair finished an amazing four-hole run that saw them match birdies on the ninth through the 12th, Laycock sank a 12-foot birdie putt at the 14th to draw even to Appleby at 12-under-par.
Appleby, meanwhile, managed to walk off No. 14 with a share of the lead after rolling in a 10-footer to save par.
But Laycock found bunker trouble again at the 15th, then blasted out to four feet and lipped out his par putt. He went on to bogey No. 16 as well, this time missing a six-footer for par to drop to minus-10.
Appleby moved three strokes ahead by making his six-foot birdie at the 16th. He hit the green in two at the par-5 17th and two-putted for his eighth birdie of the day, pushing four shots clear at 14-under.
Although a missed fairway and a bunkered approach at the 18th led to a closing bogey, the 30-year-old Aussie finished on top with a winning total of 13-under-par 271.
'To have Scotty stall at the end was fortunate on my behalf, I really thought it was going to go down to the last hole,' Appleby said. 'It was nerve-wracking all day. I was taking deep breaths from hole one.'
Four shots behind Laycock heading into Saturday's third round, Appleby charged into contention with a bogey-free 67 in difficult, windy conditions that had the rest of the field just trying to hang on.
His Sunday 65 was the best of the day and equaled the course record at The Grand.
Appleby has posted three victories on the PGA Tour in the U.S. - the 1997 Honda Classic, '98 Kemper Open and '99 Shell Houston Open. His first win on his home circuit came at the 1998 Coolum Classic.
Laycock, a regular in Japan and on the Asian PGA Tour the last few years, shot a 3-under 68 for sole possession of second place at 274.
Ernie Els, the highest-ranked player in the field at No. 4 in the world, made eight pars and a bogey on the front nine Sunday but played the inward half in 31 for a 67 and third place at 8-under 276. His back-side surge included three birdies and an eagle at the 17th.
Rod Pampling finished fourth at 6-under and Peter Lonard took fifth place at minus-four. They each had 67s.
Geoff Ogilvy, just one shot off the lead at the turn, staggered home with a 40 that featured a double bogey and a triple bogey. He carded an even-par 71 to tie for sixth with Brett Rumford at 3-under par.
American Charles Howell III tied for ninth at one-under, one stroke ahead of Adam Scott. Denmark's Thomas Bjorn finished at 2-over, while Robert Allenby, the winner of last week's Australian PGA Championship, finished alongside amateurs Chris Campbell and James Nitties at 3-over.
Full-Field Scores From the Holden Australian Open