Stanco, 31, came second to Guatemala’s Adriana Ruano Oliva, with Australia’s Penny Smith taking bronze.
“The emotion I feel is indescribable,” said Stanco after the contest, crying in the arms of her sister Cristina.
“I can’t wait to put the medal around my neck.
“I always believed I could do it.
“I worked hard to get here and now it’s beautiful.
“Ruano Oliva was unbeatable today, she shot very well.”
The Italian team made up of Luca Chiumento, Luca Rambaldi, Andrea Panizza and Giacomo Gentili came in behind the Netherlands in the quadruple sculls, with Poland taking bronze.
Italy also grabbed a gold, silver and bronze on Tuesday.
The women’s epee team beat France 30-29 to claim Italy’s third gold at the Summer Games.
Italy’s epee team celebrates their gold medal. (Photo: AAP)
Meanwhile, the Italian women’s gymnastics team won a historic silver medal.
The Italian team finished 5.802 points behind the US team spearheaded by Simone Biles, matching the only Olympic silver Italian gymnasts had ever won - in Amsterdam in 1928.
Also on Tuesday night, Gregorio Paltrinieri, 29, won a bronze medal in the men’s 800 freestyle final, becoming the first Italian swimmer to win a medal at three consecutive Olympics.
Italy have won 13 medals at the Games so far, including three golds, six silvers and four bronzes.
ANSA