Tiger Woods carded a 68 to join Ernie Els in a tie for third at 19-under-par 273. Vijay Singh, Adam Scott and Stewart Cink were one shot further back at 18-under-par 274.
Appleby was four strokes behind Singh to start the final round and moved his way up the leaderboard with a strong front nine. Appleby, who edged Singh to win this event last year, picked up his first birdie of the day at the par-4 third and reached 17 under with a birdie at the par-5 fifth.
The Australian drilled a perfect tee shot at the reachable par-4 sixth and watched as his ball rolled onto the front of the green, coming to rest 14 feet from the hole. Appleby converted the eagle try to go to minus-19.
While his challengers were struggling on the inward half of the saturated course that experienced a four-hour delay at the beginning of the day, Appleby was steady in the wind and drained a 15-foot putt for a birdie at the par-4 12th.
Appleby then parred his next four holes before running in a long birdie putt at the par-4 17th to secure his sixth career victory on the PGA Tour and a return trip to Kapalua next season.
Kaye matched Singh early with a birdie at the third but gave that stroke back with a bogey at the fifth. He holed out for an eagle at the par-5 ninth, however, to stay in the mix and took the outright lead with a birdie at the very next hole.
The 34-year-old stumbled to a bogey at the par-4 12th to fall back to 20 under and was unable to make a move down the stretch en route to the runner-up finish.
'It's a good way to start the year,' said Kaye. 'Obviously finishing second isn't too bad.'
Woods, whose lone tour victory in 2004 came at the WGC-Match Play Championship, found trouble early with a bogey at the par-4 third. He answered strongly, however, with three consecutive birdies starting at the par-5 fifth to move to 16 under.
He added a birdie at the 12th and rolled in an 8-foot putt for a birdie at the par-5 15th. Woods then birdied the closing hole to join Els in a tie for third.
'If I can just get the putter rolling a little bit more than I did obviously this week, the ball-striking is there,' said Woods. 'I'm really excited the way I was able to control my ball all week.'
Els, who shot a 71, was cruising along over the closing holes until an errant tee shot par-5 18th resulted in a late bogey.
Singh, who was in control of the tournament throughout the week, managed a triple-bogey at the par-4 13th and was never able to recover. The top-ranked player in the world countered with a birdie at the 14th for a round of 74.
David Toms and Vaughn Taylor shared eighth place at 16-under-par 276. Sergio Garcia and Craig Parry were seven shots off the pace at 14-under-par 278.