Woodland compiled a total of 44 points for the tournament, where points were awarded for birdies and eagles and deducted for bogeys or worse.
The victory was Woodland's second in a PGA Tour event and sealed a place in next week's PGA Championship. He also won the Transitions Championship two years ago in his rookie season.
"It felt like it was meant to be this week," said Woodland. "I tried to stay calm and really focus on what I was doing."
With a big overnight lead, he was never seriously challenged on the final day, even though he managed only one birdie in his first 13 holes.
He made his only bogey of the tournament on the par-4 17th, but picked up three birdies in the last five holes, including a 58-foot chip on 367-yard, par-4 14th that dropped into the cup.
"I was just trying to get it on the green, let alone go in. It was one of the best shots I've ever hit," he said.
Byrd charged up the leaderboard to finish tied for second on 35 points with a brilliant closing round of 64 that featured seven birdies and an eagle.
"My whole mindset was just to be a little more aggressive and give ourselves chances and just free it up," Byrd said.
"And I was able to do that today getting off to a hot start. (I) just felt like I was off to the races."
Romero (69) was unable to make up any ground on Woodland but leapfrogged Brendan Steele (72), who had been second overnight but bogeyed two of his last three holes on Sunday.
He finished fourth on 33 points, one clear of Dickie Pride and their fellow American David Mathies.
(Reporting by Julian Linden in New York; Editing by Peter Rutherford)
