Day, whose halfway total of 129 was a record for the Florida event, shot a one-under closing round of 71.
Northern Ireland's Graeme McDowell and Rory McIlroy finished at eight and seven under respectively, while England's Justin Rose was five under.
American Justin Thomas bettered his third-round 75 by 10 shots on Sunday to finish on 10 under in a tie for third. Rose also shot one of the day's best rounds, but his 66 was only good enough to move him into a tie for 19th.
Day dropped two shots on the front nine, but birdied the 10th and 12th to get back to level par for the round.
The US PGA winner also birdied the 16th after a superb chip to the green as he earned his 10th PGA Tour title.
