Slater scored a perfect 10 on one wave with a full-rotation aerial move, but it was the patient Fanning who finished on top with 18.80 points to 18.07 for Slater.
"Kelly did that Hail Mary for the 10 and I thought, 'Oh, here we go,' but I just caught [good] waves and I'm stoked it all paid off," said Fanning, who moved into third place in the early season point standings on the Association of Surfing Professionals tour.
"I knew there were going to be a lot of waves with the tide dropping out and I guess I just wanted to be on the good ones," Fanning said. "You've got to just believe in your judgment."
Slater's second place was enough to move him back into the lead in the points standings ahead of Adriano de Souza of Brazil.
Fanning made the finals by beating fellow Aussie Joel Parkinson in the semis. Slater advanced with a win over Frenchman Jeremy Flores.