Fowler trailed overnight leader Charley Hoffman by seven shots but made eight birdies in a dazzling front nine to lead at the turn.
He added three more birdies to break the tournament and course records at Albany Golf Club in the Bahamas and win by four strokes over Hoffman.
Woods carded a four-under 68 in the final round and was playing his first tournament since withdrawing from February's Dubai Desert Classic with back spasms.
He eventually finished tied for ninth in the 18-man unofficial PGA Tour event, but the signs are encouraging for those fans wishing to see Woods back to somewhere near his former self.
While Woods will be cautious after previous comeback attempts proved short-lived, he can take encouragement from having beaten the likes of US PGA champion Justin Thomas, US Open champion Brooks Koepka and world number one Dustin Johnson.
Elsewhere, England's Tommy Fleetwood carded a five-under 67 to finish tied third with world number two Jordan Spieth, six shots off Fowler.
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