Third-round co-leader Thompson ended with a birdie to finish at 9-under 271, two strokes better than the late-charging Ogilvy.
He overcame blustery conditions at PGA National to turn in three birdies and an eagle after missing the cut in three of his previous four tour starts this season.
Ogilvy birdied two of his last three holes, but came up a bit short of pay dirt with a final-round 69.
Rookie Luke Guthrie, who along with Thompson was the overnight co-leader, stumbled to a 3-over 73, finishing alone in third place at 5-under.
Celebrity Couples of 2014 [PHOTOS]