Luck had made only four cuts from 10 events this season, earning $US89,830 ($126,893), but found some form late last month with a tied 25th in Puerto Rico.
Englishman Casey thought his biggest challenge would be from Dustin Johnson, who was one shot behind after the third round.
Instead, the world’s No.1 player failed to make a single birdie for the first time in 31 tournaments worldwide and his three-over 74 dropped him to five under and a share of sixth.
The real challenge was the Innisbrook Resort golf course, so tough that no one shot better than 68 in the final round.
Kokrak (71) and Oosthuizen (69) each had a share of the lead on the back nine.
Long-hitting American Kokrak was tied with Casey playing the final hole but missed an eight-foot par putt.
South African Oosthuizen (69) rued a bogey at the 16th hole.
Casey was in a fairway bunker on No.18 when he hit to just over 20 feet and two-putted for the win.
The 41-year-old Casey became the third European winner in the past three PGA Tour events, following Francesco Molinari (Arnold Palmer Invitational) and Rory McIlroy (The Players Championship).