Judges awarded Molfetta the victory after he and Gabon's Anthony Obame fought a tense final that was still tied up after an overtime round. Obame's silver is Gabon's first-ever Olympic medal.
Molfetta, 28, a Rome police officer has twice won silver in the world championships. Molfetta fought strategically on Saturday, jumping to land head kicks on his taller opponents and ducking out of the way before counter-attacking.
The bronze medals were won by Cuba's Robelis Despaigne and China's Liu Xiaobo.
Quebec City's Francois Coulombe-Fortier lost his quarter-final match.