The 31-year-old world number 229 began round four one ahead of Phil Mickelson and finished with a 19 under total.
He holed from a bunker to eagle the sixth and overcame a double bogey at the 14th to shoot a two-under 70.
Mickelson, seeking to match Walter Hagen’s 45 PGA wins, birdied three of the first six holes but faded to a 74 and finished five shots back in third.
Taylor’s only previous PGA Tour win came in 2014 at the Sanderson Farms Championship.
After four shots went in as many holes on the back nine, he birdied two of the next three, with a magnificent tee shot to four feet at the 179-yard 17th.
“To do it in that fashion, playing with Phil, gives me a lot of confidence going forward,” said Taylor, who led the tournament on all four days.
The victory earns Taylor a place in April’s Masters at Augusta.