Both men had finished locked on 146 targets out of 150 and Cernogoraz was seen in tears after he ensured Croatia's second Olympic shooting medal following the bronze won by Snjezana Pejcic at the Beijing Games.
He had time to regain his composure watching Fehaid Aldeehani of Kuwait take bronze by beating Australian Michael Diamond in another shootoff after they tied on 145.
After five perfect shots, Fabbrizi missed with his sixth in the sudden death decider. Cernogoraz then brought up pink smoke on the last orange clay and fell on his back in delight.
"It is very good for me, for my family, for the country. It is the first gold medal in the sport for my country. It is fantastic," Cernogoraz told reporters after the 15th and final shooting gold of the Games was placed around his neck.
"When I finished the final I knew the silver was 100 per cent so I was very, very happy," the Croatian said to explain his earlier tears. "I didn't expect it. I thought I could get to the final but not win it."
Pejcic, who won her medal in the 10m rifle four years ago, was on hand to hug Cernogoraz after the ceremony.
The tall 29-year-old, who waits tables in his family's restaurant, had started the final in sixth and last place after his 122 from 125 targets at the Royal Artillery Barracks where he struggled in the rain on Sunday.
But he turned the tables by hitting 24 out of 25 in strengthening wind as his opponents struggled to hit the clays that were fired from one of 15 underground machines at various heights, angles and speeds.
"I'm maybe a little more famous in Croatia after this but I do not see why it should stop me helping in the restaurant," Cernogoraz said.
The 34-year-old two-time trap world champion Fabbrizi struck 23 of the targets in the windy final to take a silver medal he was overjoyed with.
"Someone had to make a mistake sooner or later," the Italian said of the shootoff through a translator.
"Unfortunately it was my turn to do that. It would have been almost impossible to win today, it was the Croatian's day."
Aldeehani was also delighted to be on the podium after the disappointment of missing out on a medal in the double trap when his gun broke and he missed seven targets in the final with a borrowed gun.
"The double trap loss helped me today. I was very unlucky that day. Today I was lucky. The people of Kuwait and the Arab nations will be proud and inspired," the 45-year-old father of four told reporters.
Diamond had already trudged off after a bout of nerves strangled the twice Olympic gold medallist's chances of adding a third. He went though the qualifying sessions with a perfect score only to be the worst performer in the final, missing five targets.
"The wind played some part," said the Australian, who missed two key shots back-to-back from the 21st shot.
"It was really disappointing as that was a silver medal or gold medal shot."