Johnson held a three-stroke entering Sunday's Round 3, but stumbled into fourth place two shots off the pace with a 74.
He came back in a big way Monday, tying Billy Horschel for the low round of the day with seven birdies and no bogeys on the Plantation Course at Kapalua Resort.
The 37-year-old finished at 19-under-par 273 to claim his 11th PGA Tour title.
Co-overnight leader Jordan Spieth carded a 4-under 69 to take second place at 18-under.
Simpson, who had also shared the lead after 54 holes, logged a 70 to tie for third at minus-17 with Kevin Streelman.
Fifth place went to Jason Dufner (69) at 15-under.
Swim Week Miami Beach 2014 [PHOTOS]