It was the second medal at a major competition for the 22-year-old Szilagyi, who beat defending champion Man Zhong of China on his way to the final. Szilagyi won bronze at the 2011 European Championship in Sheffield.
"I have never been this happy before," said Szilagyi, who is ranked sixth by the International Fencing Federation. "During the day, I forced myself to think that it's just a competition, not the Olympic Games. Now that it's over and I have the gold medal, I am just unbelievably happy."
Nikolay Kovalev of Russia earned bronze with a 15-10 victory over Rares Dumitrescu of Romania, the 2009 world championship silver medallist .
It was Kovalev's first individual medal, though he has been part of the Russian team that won gold in the saber team event at three straight world championships from 2010-12.
In the quarterfinals, Kovalev ousted top-seeded German fencer Nicolas Limbach 15-12 in a tense match.
Limbach joined an early exodus of title favourites. World and former Olympic champion Aldo Montano lost 15-13 to Occhiuzzi, Russia's main medal hope Alexey Yakimenko was upset 15-14 by Daryl Homer of the United States, who then lost to Dumitrescu, and fourth-seeded Bongil Gu of South Korea lost by the same score to Germany's Max Hartung.
Despite the big names failing to deliver, Szilagyi didn't start eyeing the gold until the final was well under way.
"I only thought of winning when I led 8-1 against Diego," Szilagyi said. "Then I realized everything I was trying today worked out well. If you think you can win, it makes you feel relieved."
Occhiuzzi failed to earn Italy a second straight fencing gold after Elisa Di Francisca won the women's individual foil Saturday. It did not dampen his excitement.
"This is a real dream coming true," said Occhiuzzi, who won bronze in the saber team event at the 2008 Beijing Games. "I have always been the underdog in the Italian team, but I knew what I was capable of. It's fantastic that I could prove it today."
That the top four went out at an early stage did not really surprise Limbach.
"These are the Olympics, this can happen," the German said. "It shows you how tight the top in saber really is ... I knew the medals were not just there to be picked up."
Limbach struggled to find his way into the match against the very attacking Kovalev, who went 4-0 and later 7-3 up. Limbach seemed to have found his stride as he scored five straights points. Later he rallied from 9-12 down to level at 12-12.
"I never felt I had the momentum with me," Limbach said. "I had to fight hard for each of these points. He left me few opportunities to play my own game and he had some really good attacks."
World champion Montano missed over one month of training building up to the Olympics because of a left-thigh injury. He battled back from 11-5 down to trail by just one point at 14-13 before Occhiuzzi closed out the victory.
"I was afraid to tear the muscle so I tried to stay on the defensive side," Montano said. "Occhiuzzi knew of my problems and rightly took advantage."