Chris Paul had 16 points and six assists for the Hornets (3-2), who used a 19-9 run in the third quarter to tie the game 67-67.
Jackson scored 12 points in the fourth quarter as the Hornets outscored Miami 25-18.
Miami centers Shaquille O'Neal, Alonzo Mourning and Michael Doleac all skipped the trip to the Mississippi coast because of injuries. Guard Dwyane Wade continues to recover from offseason shoulder surgery and also didn't make the trip.
Udonis Haslem had 20 points for the Heat (0-5), while Jason Williams added 19 and Smush Parker 12.
Tyson Chandler finished with 11 points for the Hornets, while David West and Rasual Butler both had 10.
Members of the Hornets organization spent most of Friday at the Salvation Army in Biloxi, providing assistance to 800 families who were victims of Hurricane Katrina. Like New Orleans, Mississippi is still recovering from the devastating storm two years ago.