Johnson, who started the final round two shots off the pace, took the sole lead with a short birdie putt on the 14th hole and also birdied the next two holes to pull away at the Kapalua Plantation course.
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 (£0.7m) for his 11th PGA Tour victory. Since his first victory nearly a decade ago, only Tiger Woods, Phil Mickelson and Vijay Singh have won more often than Johnson on tour.
It was a second successive victory for Johnson, who ended last year by beating Woods in a playoff at the world number one's World Challenge in California.
The Tournament of Champions was the first PGA Tour event of 2014, but the seventh official tournament of the season, which started in October.
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- Tiger Woods
- Kevin Streelman