Watney (31) became the second player in two days to flirt with a magical 59 at the par-71 Mines Resort and Golf Club, before bogeying the last as the pressure told.
But his 10-under-par round was enough for a thrilling one-shot win, while Van Pelt botched a chance to force a play-off on the 18th – the same hole where he also missed a 59 on Saturday.
Robert Garrigus birdied the last two holes to share second with Van Pelt, while Woods, the 14-time Major champion who had threatened to steal the show, finished tied fourth with Brendon de Jonge and Chris Kirk.
Woods, starting the day five shots off the lead, had roared into contention with six birdies in his first 10 holes, and he picked up two more shots in his last three holes for a 63.
But Watney, turning at five under, added another six birdies up the back nine and despite his lone bogey on 18, finished with 22-under 262 for his sixth victory in a PGA Tour-sanctioned event, and his second of the year.
Van Pelt needed a birdie on the last hole to set up a play-off, but he put his tee shot onto an adjacent fairway and then bunkered his recovery, before scrambling to save par.
Woods, who now heads to China for Monday's one-round exhibition event with world number one Rory McIlroy, was left to rue a stumbling back nine on Saturday which cost him the chance of victory.
"I'm very pleased with the way I played. I hit the ball well and hit a bunch of putts today too. So overall it was a good day," said Woods.
"I had to shoot nine under today just to have any kind of a chance. Yesterday's nine holes put me in a spot where I couldn't win the championship."
Woods had pledged to be aggressive and he attacked from the off with a massive drive which landed just short of the green on the 363-yard, par-four first hole, then chipped and putted four feet downhill for birdie.
His tee-shot on the par-three second drifted slightly left, but from the fringe Woods caressed a sand wedge down the slope and slowly into the hole for a fist-pumping birdie.
On three, he found himself the wrong side of a greenside bunker but another stunning chip, from a downhill lie, put him three feet from the pin for his third birdie in a row.
With heat haze visible on the sixth green, Woods sent a ruler-straight pitch shot from 90 yards to within three feet to pick up his fourth shot of the day, accompanied by huge shouts from his big crowd of following fans.
At the seventh he putted from the collar, 10 feet down a steeply sloping green, for his fifth birdie, and picked up another on the 10th to go 17-under and two shots back from joint leaders (Chris) Kirk and (Bo) Van Pelt.
But echoing his round on Saturday the hot streak cooled and Woods had to escape from a bunker on 15 before his next birdie, courtesy of an unerring tee-shot on the par-three 16th. Another birdie on 17 was his last.
Meanwhile, Carl Pettersson was in the clubhouse with a nine-under-par 62, and Watney had raced up the leaderboard with seven birdies over his first 12 holes – including five in a row around the turn.
Watney seized the lead with another birdie on 13 and put himself in the driving seat with three in a row from 15 to 17, going 11 under for the day.
The 59 was on – but Watney wilted on the last hole, carding his only bogey of the day in front of the heaving clubhouse gallery.
Behind him Van Pelt, playing in the final pair, birdied 15 and 17 to be just one shot behind going into the final hole, setting up a nerve-shredding finish.
But a day after his bid for a 59 had faltered on the 18th, Van Pelt sliced his tee shot onto the 10th fairway and then shot into a greenside bunker before getting up and down for par. – Sapa-AFP