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 defending champion Bo 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 place with Van Pelt, while Woods, the 14-time Major champion who had earlier 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.
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