He finished at 20-under 268, while American Finau (69) birdied the last to claim second place on 16 under.
Englishman Justin Rose (65) was another shot back in third.
Swede Stenson faded with a 71 to finish six shots back in fourth place in the elite 18-man field.
Finau hung within striking distance of Rahm until a poor tee shot at the 14th led to a double bogey and pretty much sealed the deal for the Spaniard.
"I can say that ball-striking-wise it's pretty much where I want it to be," a satisfied Rahm told Golf Channel.
"It's about as perfect as it could have been today. I played so solid tee to green, didn't make any mistakes.
"If you can capitalise on the five par-fives and the two driveable par-fours, which I did on all of them today, you can have a good chance and that's what happened."
Rahm was part of the winning European Ryder Cup team in September and played his part by beating Woods in the singles.
"That Sunday with Tiger is still the most emotional, most important moment of my golf career," said Rahm, 24, who has been ranked as high as second in the world in his still young career.
"I pretty much started crying when I was shaking his hand 'cause that meant so much to me to play against Tiger Woods in the Sunday match.
"A couple of months later to win his foundation's event, this is really special."
Rahm's victory is unofficial on the PGA Tour, though the tournament awarded world ranking points.
Tournament host Woods finished second-last, a distant 19 strokes behind Rahm.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Clare Fallon)
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