Bradley carded a 2-under-par 70 for an overall score of 14-under 274 in his third win on tour and first since the 1998 Doral-Ryder Open.
Quigley birdied five of his the last 10 holes for a 67 and Day, who had shared the third-round lead with Bradley, shot 71 to tie for second at 13-under 275.
Bradley won $630,000.
"It's been so long since I've been there. But you know, my short game was good this week; it cured some ills that I had," Bradley said. "I'm almost 43 and you don't know really know how many opportunities you're going to have."
Swim Week Miami Beach 2014 [PHOTOS]