Appleby made birdie after knocking a bunker shot within tap-in range at the 660-yard 18th hole, becoming the first player to three-peat here since Gene Littler did it from 1955-1957. He and Singh both ended at 8-under-par 284 for the tournament.
This victory was especially impressive, given the slew of high scores carded throughout the weekend by a field of 2005 winners.
Including Appleby and Singh, just six players finished under par after four rounds.
'There wasn't really any momentum out here this week -- it was just so tough,' said Appleby.
Singh made a mockery of the windy conditions Sunday, strolling to a round of 7-under 66 that included four birdies on his final seven holes. It was by far the best round turned in at Kapalua's Plantation Course (Olin Browne carded the only other round in the 60s -- a 69 on Thursday).
'I didn't know [what Singh shot] until I got up on the 15th green, and I was like 'Excuse me?' I had to double check it,' said Appleby, who finished with a final-round, 2-under 71.
Singh began the day in a tie for fifth place at minus-1, but he played his first 12 holes at 5 under and joined Appleby and Michael Campbell atop the leaderboard at 6 under after a birdie at 12.
Singh's best shot of the weekend came at the par-4 12th -- a spectacular bunker shot that set up his tap-in birdie.
Campbell, the reigning U.S. Open champion and Appleby's playing partner, soon fell off the pace after a double bogey at 12, while Appleby regained his lead with a birdie at the same hole to reach minus-7.
That made it a two-horse race, but Appleby was forced to play catch up after a bogey at 13 and routine par at 14 dropped him two strokes off Singh's pace.
Appleby rebounded, however, by matching Singh's birdie at the par-5 15th and then carding two straight pars to head to 18 trailing by one.
Singh was already at the driving range after finishing off his 66 with an 18-inch birdie putt at the final hole, so he wasn't watching when Appleby made birdie from the fairway rough on 18 to tie him. Appleby chipped within 4 feet to set up the putt.
Both players found the fairway back on 18, with Singh about 15 yards further out.
Appleby then pulled a 3-iron and watched as it hit the front of the green, gained speed and rolled into a bunker past the hole. Singh knocked his second just shy of the green, then putted within 8 feet.
But it wasn't good enough, because Appleby's ball was sitting high enough in the sand to allow him to attack the pin.
He did, and the ball rolled just past the right edge, landing within 18 inches to set up an easy putt and the $1.08 million winner's check.
Said Singh afterward, 'I did everything good except make one more putt.'
Jim Furyk made a nice late run to finish alone in third place at 4-under-par after a final-round 72. Campbell stumbled to a 2-over 75 and tied for fourth place with Vaughn Taylor, who shot a 71 on Sunday.
This season-opening event was reserved for PGA Tour winners from 2005. Four of those winners -- Tiger Woods, Phil Mickelson, Retief Goosen and Padraig Harrington -- qualified, but elected not to play.