Italy, who have never before won Team gold at the Games, were nine behind with one shot remaining when Frangilli struck centre gold.
The dramatic 219-218 win for Frangilli, Mauro Nespoli and Marco Galiazzo against Brady Ellison, Jacob Wukie and Jake Kaminski capped a day of surprises in the competition, with favourites Republic of Korea losing 224-219 to the USA in the semi-final.
USA finished with the silver, while the Koreans saw off Mexico to take bronze.
Frangilli was overjoyed after the Victory Ceremony and reflected on the culmination of an Olympic story that began with his bronze in Atlanta.
'This was a very hard fought medal, I've been chasing it for 16 years,' he said.
'It is a dream come true. It is a very strong emotion and to score 10 with the last arrow, that is the dream.
'I knew I needed a 10 and I felt incredible pressure so I decided to empty my head of everything. I tried to give all I had to give. When I heard '10' I was excited.
'I have no words to describe what I feel. When we came here we were not sure if it was possible.'