The American finished with a one under par 69 to finish nine under for the week and win by two shots from Australian Geoff Ogilvy at Palm Beach.English pair Lynn and Justin Rose were the pick of the European Tour contingent – both players finishing in a tie for fourth on three under after rounds of 69 and 71 respectively.
Both Thompson and Ogilvy earned their places at next week's WGC-Cadillac Championship at Doral Country Club with their results.
Thompson and playing partner Luke Guthrie – who eventually finished third - shared the overnight lead on eight under and though the former saw a long birdie putt at the second just dive left, he opened up a three stroke lead inside the first five holes.
A monster eagle putt at the third sparked his run as, though he dropped a shot at the next, he birdied the par-three fifth to return to ten under, while Guthrie wasted a birdie at the third with bogeys at two and five.
Two dropped shots sandwiched a birdie as Thompson reached the turn nine under and Guthrie also slipped back with a bogey at the tenth.
The latter birdied the 13th to bring the gap back to two shots but the decisive moment came at the next as the second-year professional hooked his drive out of bounds and racked up a double-bogey six.
That left Thompson four clear heading into the Florida course's feared "Bear Trap", holes 15 to 17, and he safely found the green at the first of those holes before almost holing another long putt. Guthrie's birdie attempt slipped left, though, to keep the margin at four.
Thompson was again on in regulation at the next and Guthrie responded with an aggressive shot from a fairway bunker to the back fringe, 15 feet from the hole. Guthrie got down in two but Thompson showed the first sign of nerves, overhitting a four foot putt which hit the right edge and stayed out.
Ogilvy, who had flown under the radar with pars until dropping a shot at the 14th, holed from almost up against the grandstand at 16 to go six under but after an aggressive tee shot at the next, he underhit the birdie putt which would have taken him within one.
Thompson made a solid par at 17, despite a whoop from a lone spectator as he putted, and Guthrie missed from inside three feet.
And needing only to find two-putt range from a greenside bunker at the last, Thompson sent his pitch rolling to within six feet and rattled in the putt for a two stroke win.
He said: "It was just about sticking to my game plan. All through the week I'm just trying to find it in the dirt.
"This week was magical, I kept feeling it, kept believing - my wife was super-encouraging and all in all it's just a wonderful experience."
Ogilvy birdied the last to finish seven under, and one under for the day.
He said: "I played really well, it was a little frustrating with the putter but I was happy with how I hit the ball. Anything under par out here is a good score today
"It's probably not as dramatic as it looks but it's a nice bonus. I thought 'this has to go in' and then it hangs on the edge, then it drops to give me a chance."