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More usually contenders for the competition's wooden spoon, Italy proved their victory over the French two seasons ago was no fluke as they defended well and took their chances against the 2011 World Cup runners-up.
Tries from captain Sergio Parisse and Martin Castrogiovanni, plus 10 points from man-of-the-match Luciano Orquera and three from substitute Kris Burton led them to victory, just their third ever over the French.
France were far from their best and despite tries from Louis Picamoles and Benjamin Fall and eight points from a rejuvenated Frederick Michalak, they were deservedly beaten by Jacques Brunel's effervescent side.
"I'm really happy for the team and the fans, after two years we've beaten France again in Rome," Orquera told reporters.
"We were mentally extremely strong right from the beginning, we wanted to win at any cost and we were always in the match. We never gave up."
Italy joined England and Ireland on two points and sit in third place after the first round of games, which included another upset as holders Wales lost 30-22 to Ireland on Saturday. A fired-up England were 38-18 winners over Scotland.
Italy captain Parisse led from the front, putting his team ahead with only four minutes gone with a spectacular counter-attacking try.
The move was started when Luke McLean recovered a France kick and burst through the first line of defence. The ball was fed to the magnificent Orquera, who offloaded to his captain and then converted the try.
France responded with intense pressure, and a try bundled over the line by Picamoles looked to have levelled the scores, only for Michalak to miss an easy conversion.
Orquera extended Italy's lead to 10-5 with a smart drop goal on the quarter hour and the number 10 continued his hot form three minutes later with a converted penalty given for Maxime Mermoz's offside offence.
Italy's defence did brilliantly to hold back France's powerful attack in the first half hour, only conceding a 27th-minute Michalak penalty after France had a Yoann Huget try denied by the TMO a minute before.
However, Philippe Saint-Andre's team took the lead three minutes later, Benjamin Fall taking the ball from Huget and scoring a try under the posts which Michalak had no problem converting to give France a 15-13 halftime lead.
Flyhalf Michalak, who was brought back into the international fold by Saint-Andre last year after several seasons in the wilderness, gave France a five-point advantage with a penalty for collapsed scrum with 50 minutes gone.
He nearly made it eight two minutes later when he narrowly missed another penalty from near the halfway line.
France looked to be dominating but a sudden burst of pressure from Italy resulted in Castrogiovanni scoring his 12th international try on 56 minutes which was comfortably converted by Orquera for a 20-18 scoreline.
Burton, who replaced Orquera as flyhalf, gave his side a five-point lead 12 minutes later with a deft drop goal which had Italy fans dreaming of a repeat of their 2011 heroics when they beat France 22-21 for their first Six Nations win over them.
As the match moved to its close, France turned the screw, and with a minute left Davide Giazzon was sin-binned, leaving the home fans to suffer for the excruciating final seconds of last-ditch defending.
But with a huge crowd roaring their team on they kept their opponents at bay for an incredible win and a dream start to the Six Nations for their French coach Brunel against his countrymen.
"I was in emotional turmoil the whole match," Brunel told reporters. "France are a great side and it's never an easy game. The match could have gone either way as we saw.
"The team has really grown and today they demonstrated their strength. It's the right time to manage Italy."
France manager Saint-Andre was left to reflect on where it had all gone wrong.
"We lacked precision and accuracy. We didn't take advantage of our chances while we were in the lead and the Italians overtook us," he told reporters.
"The first half an hour was bad and the last half an hour was a catastrophe. It hurts but it's only one game. What we have to do now is concentrate on the Wales match on Saturday."