The win was the fourth on the PGA Tour for Johnson, who finished at 19-under 261.
Johnson won $810,000. It was his first victory this year.
"I have not put things together this year," Johnson said. "I putted pretty well this week though. A lot of work over the last six weeks has paid off."
Wi shot a 9-under 61 to gain a share of second with Wilson (63) and Wilkinson (64) at 264.
Jeff Overton (65) was fifth at 265. Stephen Ames (62) and Chris Stroud (68) shared sixth at 267.
Rory Sabbatini, the third-round leader, slipped to a 72 and tied for eighth at 268 with Pat Perez (65) and Tim Herron (69).
Swim Week Miami Beach 2014 [PHOTOS]