Singh finished with a three-under 70 to end the event at 21-under-par 271. Darren Clarke finished a distant third at 17-under-par 275.
'The end of last year, I really tried to switch off for the little period. I had to have a break. I guess that wasn't something I was doing when I was having a lot of seconds,' said Appleby, who has finished in the top-two in four of his last six events. 'I was just nose to the ground and go. I think my game was really inside me this week. I felt very confident the way I was hitting it.'
Appleby held a two-shot lead entering the day and with his play on the front nine, it didn't look like he would have any trouble holding that lead. However, Singh caught fire on the back nine to put pressure on the Australian.
Appleby rolled home back-to-back birdies from the fourth to climb to minus-22 and gain a five-stroke lead as Singh had dropped a stroke on No. 2.
The lead continued to grow from there. Appleby went birdie, bogey, birdie from the seventh, while Singh bogeyed No. 8 and birdied No. 9 to give Appleby a six-stroke cushion heading to the back side.
From there, it started to get interesting. Appleby managed just back-to-back pars from the 10th before dropping a stroke on No. 12 to fall back to 22- under.
Singh opened the back side with four straight pars. The Fijian, who ran off seven birdies in a row to end the second round, began to make his move at the 14th.
He made birdie there to get within four shots of Appleby. Singh got up-and- down for birdie on the par-five 15th. He then made the first birdie of the day on the 16th to close within two shots.
Appleby, who was inside Singh on the 16th green, could only manage a two-putt par. He did the same at the next hole, as did Singh, sending the two to the last hole with Appleby ahead by two.
Both men hit huge drives on the 663-yard closing hole on the Plantation Course at the Kapalua Resort. The duo both missed the green short to the right.
Appleby pitched his third within 15 feet of the cup. Singh, electing to putt from the fairway, nearly rolled home a monstrous eagle putt, but his effort narrowly slid by the right edge.
Appleby, who led the field this week averaging 27.5 putts per round, calmly two-putted for par and Singh's tap-in birdie meant only that he finished one- shot back instead of two.
'Vijay hadn't really made much at all on the front nine, but I did realize that Vijay was never going to go away,' said Appleby, who claimed $1,060,000 for the win. 'It was looking like the cards were falling my way with him missing and me making a couple.
'By the same token, I knew I just had to do my own thing. Then Vijay closed in with some birdies, some very good birdies. I didn't make any mistakes. Eventually to my benefit, he ran out of holes to really catch me, and I just had to really play smart coming in in pretty trying conditions all day.'
'I didn't get a lot going on the front nine, you know, I played it two-over, and you can't do that,' said Singh. 'I had a lot of chances but Stuart played really well. He made the putts that he needed to and he deserved to win.'
Singh, who had nine top-two finishes last season, gave it a go on the 72nd hole, but his putt just missed on the right edge.
'I just said give it a go, you never know,' said Singh, who played the three par-threes in four-over par. 'The putter took a lot away from me this week, but I thought it owed me one. The putt looked good for a long time, but it broke away at the end.'
Tiger Woods and Retief Goosen shared fourth place at 15-under-par 277. The $275,000 paycheck for Woods put him over the $40 million mark for career earnings with $40,052,265. He is the first golfer to reach that plateau.
Kirk Triplett finished alone in sixth place at 14-under-par 278. Adam Scott finished one stroke behind him at minus-13. Scott Hoch closed with a 72 to end at 12-under-par 280.
Davis Love III, who bombed a 476-yard drive on the 18th hole Sunday, the longest drive of the week, shot a 72 on Sunday to share ninth place with Ben Crane at 11-under-par 281.