Darren Clarke stands alone in second place at 6-under-par 67. Kirk Triplett, Scott Hoch and Justin Leonard share third place at 5-under-par 68.
Appleby did not get off a great start. He needed to take a penalty drop on the first hole and that led to a bogey. The Australian recovered with back-to-back birdies from the fifth to head to the back side of the par-73 Plantation Course at Kapalua Resort at 1-under.
The 32-year-old caught fire on the back nine. He rolled home a birdie at the 10th and followed by dropping a 9-iron within four feet to setup birdie at the 11th.
Appleby made it three straight as he drained a birdie from within 10 feet at the 12th. He got up-and-down for par from just off the green at the next.
He then converted consecutive birdies from the 14th to climb to 6-under. Appleby closed out his round by rolling in a 12-footer for birdie at the last.
'This is an unusual wind, very unusual. It's probably the easier wind, I think,' said Appleby, who won the Las Vegas Invitational last season. 'Not the usual wind. A little different to what we'd seen all week. I was pretty unfamiliar with it because I haven't been here for four years.'
Appleby, whose last win before Las Vegas came at the 1999 Shell Houston Open, is glad to be back at this event.
'You say it's nice, you had a good season, it's an honor to play here, it's a privilege to play here, you're playing with the best players of the previous year,' said Appleby. 'I don't think any player can deny that.'
Clarke, who won the 2003 WGC-NEC Invitational, also bogeyed the first hole when he was unable to get up-and-down for par from a greenside bunker. He ran off three straight birdies from the fourth to get to minus-two.
The Ulsterman got up-and-down for birdie on the ninth, then drained a shot from over 60 feet out from the back edge of the 10th green to climb to 4-under.
He continued his move up the leaderboard when he dropped a 4-iron within 15 feet for birdie at the 13th. At the last, Clarke two-putted for birdie to close at 6-under.
'Towards the end of last year, when I was trying to get myself into shape, my hand-eye coordination went out a little bit, I just got out of sync,' Clarke said. 'Because of that, I was not hitting the ball well.
'Having the layoff, coming back, hitting balls here, I seem to have gotten it back a little quicker than I thought. Today was very positive from that point of view, hitting the ball as well as I did, and giving myself as many chances. That's the whole reason why I'm trying to get in better shape.'
Clarke, who has dropped several pounds and quit smoking, is in as good a shape as he has ever been.
'Today walking up and down the hills, I was fine,' said Clarke. 'It was my first ever competitive round, I think, without having any nicotine in my body. That was another first. No beer, no nicotine. Don't know what's going on really.'
Fred Couples, John Huston, Davis Love III, Shigeki Maruyama and Adam Scott share seventh place at 4-under-par 69.
U.S. Open champion Jim Furyk carded a 3-under-par 70. He is joined there by Retief Goosen, Peter Jacobsen, J.L. Lewis and PGA Championship winner Shaun Micheel.
Tiger Woods finished one stroke further back at 2-under-par 71 after sinking an eagle at the par-5 closing hole.
Defending champion Ernie Els birdied two of his last three holes to finish at even-par 73.