Di Francisca, who was the 2010 world champion, upset top-ranked Nam Hyun-Hee of South Korea by the same score in the semifinals.
"This is very emotional for me," Di Francisca said. "The final was very, very difficult. I went from 'I want to win' to 'I don't want to win' to 'I want to win.' I was just afraid of winning. Errigo is a very strong player and we both know each other so well."
Di Francisca changed her tactics for the final and chose a less attacking approach than in her previous matches.
"Normally, I play more like a tiger, but in the final I calmed down," Di Francisca said.
In the other semifinal, Errigo beat three-time defending champion Valentina Vezzali 15-12, denying her Italian teammate a change to become the first female athlete to win individual gold at four consecutive Olympics.
Vezzali then won a tense battle for bronze 13-12 against Nam.
"It was such a tough battle for the bronze medal, but in the end I managed to get it, although my goal was of course to get my fourth gold in a row," Vezzali said while fighting tears. "I wanted to win that fourth gold so badly."
The 38-year-old Vezzali won gold at every Olympics since 2000. With another gold medal, she would have equaled the record held by three male athletes — sailor Paul Elvstrom of Denmark, discus thrower Al Oerter and long jumper Carl Lewis, both of the United States.
Vezzali still got a standing ovation from the crowd after coming back from 12-8 down against Nam. She equalized in the final second of the nine-minute regulation before winning the sudden-death point in extra time.
"It was just 10 minutes after I lost the chance for a gold medal," she said. "It was hard to be motivated again. I have to thank all the Italians in the audience, who were a great support for me."
Vezzali, who was the flag bearer for the Italian time at Friday's opening ceremony, rejected suggestions that the missed chance for another gold could mark the end of her illustrious career. She didn't rule out competing at the 2016 Olympics in Brazil.
As the top-ranked woman in the world, Vezzali started as favourite in the foil competition. Her first real test came in the quarterfinals against Ines Boubakri of Tunisia, a match she won 8-7 in extra time.
After scoring the decisive point, she fell on her back in celebration and screamed with excitement.
"Today it was very difficult," Vezzali said. "For me, it's the fifth Olympics and the pressure to win was building more and more."
Her hopes of the Olympic record were then shattered by Errigo, whose silver medal in her first Olympics did not make her too excited.
"My dream was the gold medal so I am sad," Errigo said. "To lose the final by one point is not nice. But I have to be happy for this."
The sweep of the podium makes Italy a strong favourite for the title in the women's foil team event.
"In the Olympic Games, everything is possible," Vezzali said. "Let's see what happens."