Overnight leader Casey eked out a one-over-par 72 in the final round, which was good enough to fend off his rivals in demanding, breezy and firm conditions at Innisbrook Resort in Palm Harbor.
After a three-putt bogey at the penultimate hole, the 41-year-old Englishman hit a tournament-winning shot from a fairway bunker to the heart of the final green.
With two putts he finished at eight-under 276 for his third victory on the PGA Tour in 250 career starts.
Long-hitting American Kokrak challenged Casey and was tied for the lead playing the final hole, but he bogeyed for a 71.
Sweet-swinging South African Oosthuizen (69) made a flying start by holing a 25-yard bunker shot for eagle at the first hole, but rued a bogey at the 16th.
Casey said the self-belief attained in winning last year had held him in good stead.
"Last year's win was so big," he told NBC television. "That felt like my first victory as a professional. I've felt so different since then, new confidence.
"I'm getting older but I feel like I'm getting better. This is so cool."
While Casey celebrated, world number one Dustin Johnson lamented a birdie-less 74 that left him three shots behind in a tie for sixth, after he had started the day one back of Casey.
Casey is the third consecutive European winner on the PGA Tour, following Francesco Molinari (Arnold Palmer Invitational) and Rory McIlroy (Players Championship).
The last time Europeans enjoyed such a streak was 2010.
Casey heads to the Masters in a couple of weeks and will certainly be part of the conversation at a tournament where he has a strong recent record. He has not finished worse than 15th there over the past four years.
He is projected to rise to world number 11, not too far off his career-high ranking of third a decade ago, before injuries and a divorce temporarily sent his game into the rough.
Casey has 56 top-10 finishes on the PGA Tour.
"I've been incredibly consistent the last few years but I would almost give up some of that consistency for more victories," he said.
"I'm not a prolific winner (on the PGA Tour) but I've won 17 times around the world. I know how to win, plain and simple.
"Today was a very different attitude to maybe (what) I had had the last three, four years. I still felt Dustin was the favourite, but it didn't mean I didn't think I could beat him.
Casey played all week with the words "THE CHAMP" on the back of his caddie's bib, instead of the usual player surname.
They were words of his choosing, after tournament organisers asked him what he would like to do.
"It means I don't need to change the caddie bib for next year either," he joked.