The 2007 Masters champion finished at 19-under 273, while fellow American Jordan Spieth (69) birdied the last to finish outright second on 18-under, with compatriots Kevin Streelman (67) and Webb Simpson (70) another shot back in tied third.
Johnson, 37, collected $1.14 million for his 11th PGA Tour victory but was subdued afterwards, his focus on Simpson’s regular caddie Paul Tesori whose newborn son is in intensive care in a Florida hospital.
“That’s where my heart was today and that’s where my mind was a lot of the day,” Johnson told The Golf Channel.
The world number nine is renowned for his wedge game, which he demonstrated by chipping in from 45 feet at the par-three second as joint overnight leader and defending champion Dustin Johnson (73) fell away with three early bogeys.
Zach Johnson then continued his good work with a series of precise approach shots on the back nine.
“I didn’t deviate away from anything I typically do on the golf course,” he said.
“I just picked it apart. It’s fairways and greens for me, trying to stay below the hole, give myself an aggressive look, trusting in what I’m doing.”
He made seven birdies, but it was a par save at the par-four 13th that perhaps was the turning point.
After hitting his first putt far too hard, he sank an eight-footer to remain tied for the lead before holing a similar-length putt at the next to go ahead for good.
Comfortable under pressure, he briefly sat to admire the panoramic view of the island of nearby Molokai after his tee shot at 17 before recording two pars to seal a second straight victory. Johnson ended last year by beating Woods in a playoff at the world number one’s World Challenge in California.
Since his first victory nearly a decade ago, only Tiger Woods, Phil Mickelson and Vijay Singh have won more often than Johnson on tour.
The final margin disguised the ease of Johnson’s win as Spieth, 20, closed strongly to claim his third runner-up finish in the past five months.
Spieth led the first PGA Tour event of 2014 and seventh of the season at the turn, but his frustration built on the back nine as the putts failed the drop until it was too late.
(Reporting by Andrew Both. Editing by Patrick Johnston)