Dual Masters champion Watson was in control throughout the final round, shooting 66 to finish at 25-under-par 263, three clear of fellow American Patrick Reed (66).
Starting with a two-shot buffer, Watson claimed control with four birdies in his opening seven holes at Albany Golf Club in New Providence before adding three more early on the back nine.
A final hole bogey was his only blemish as he claimed the $3.5 million event, which comprised an exclusive 18-man field, and offered world ranking points, though it is not an official PGA Tour event.
Rickie Fowler (64) finished third at 21-under, with world number one and defending champion Jordan Spieth (67) left to settle for fourth place, five shots back.
Woods was unable to play due to recent back surgery, but he was on site to watch the action.
“It means a lot,” Watson told reporters as he spoke glowingly of 14-times major champion Woods.
“He's the guy I looked up to, he's the guy I wanted to be like. How do you not want to be a champion like him when it comes to golf?”
In the field as a late addition after Australian Jason Day withdrew, Watson made the most of relatively benign conditions throughout the tournament, overpowering a course usually protected by brisk winds.
While his length was an obvious boon, the 37-year-old claimed it was his work on the greens he had to thank.
“I just think it's putting,” the world number four said.
Spieth, meanwhile, could not successfully defend his title, and was left to settle for fourth place, five shots back, ending his stellar calendar year during which he claimed five wins including the Masters, U.S. Open, Tour Championship and the season-long FedEx Cup.
“There is no disappointment. For a guy like Bubba, if he's driving the ball well it is a pitch and putt,” Spieth told reporters.
“I obviously had to shoot more than nine-under on the weekend and hats off to a great champion in Bubba but I am certainly pleased with how we finished off the year.
“It's a season that, for me, I now put those kind of expectations on myself each season and whether that's fair or not it doesn't matter to me, I'm still going to work as hard as I can to try to achieve the same kind of year we had this year, because it certainly was fun.”
A course record 10-under-62 by Englishman Justin Rose was only good enough to lift the former U.S. Open champion to 13th.– Reuters
Original source: Bubba wins World Challenge