The home side went ahead early on as Sergio Parisse scored a try inside five minutes and, though France got back in front, Martin Castrogiovanni finished off a magnificent team effort by Italy with 20 minutes left, a try which proved to be the decisive score.
France pushed hard to get back on terms in the final 10 minutes, but they simply had nobody who was able to cut open the superb Italian defence - and for the second time in three years, France came away from the Eternal City with a loss that devastates their Six Nations hopes.
Italy came into the match with high hopes of recreating their famous victory against the French at the Stadio Flaminio two years ago, and they got off to a dream-like start as fly-half Luciano Orquera broke the line before delivering a pass for Parisse to run in for a try.
Orquera added the extra points to put his side seven points ahead and, though France quickly pulled a try back thanks to a characteristically storming run by Louis Picamoles, Italy were in charge. Their constant pressure quickly lead to a pair of penalties and the home side were 13-5 ahead inside 20 minutes.
France were on the back foot, but the shock of falling so far behind spurred them into activity. A spell of camping inside the Italy 22m line saw Yohan Huget cross over in a bundle of bodies, but the TMO was unable to see if he had touched down and Frederic Michalak had to settle for three points to cut the deficit to five just before the half-hour mark.
Six minutes later France got their noses in front, beginning to take control thanks to a fantastic counter-attack by Huget, who timed his final pass to Benjamin Fall perfectly and allowed the winger to outstrip his chasers and touch down under the posts.
It seemed that order would be restored as France stretched their lead 10 minutes into the second half as a string of penalties given away by Italian sloppiness and indiscipline allowed Michalak to land another penalty.
Yet with 23 minutes left Italy took the initiative once more with an amazing turn of events: France number nine Maxime Machenaud produced a blistering run from just outside his own 22m to get within 10 metres of the Italian line - but he failed to hang on to the ball when tackled, and Italy hit on the break.
Almost the whole team was involved in the silky, flowing move which followed, with Orquera making the key break to get to within five metres of the line and offloading to Castrogiovanni to score.
Orquera added the conversion to put Italy into a lead that they never relinquished, and even increased when substitute fly-half Kris Burton slammed a huge drop goal over from at least 40m.
France continued to press to get back into the match but Italy's defence was simply too tough and disciplined, while the French side was atypically devoid of invention in the crucial phases despite the introduction of the ferocious Mathieu Bastareaud.
Italy held on bravely for a victory that was if anything even finer than the one they won at Stadio Flaminio two years ago: then, they were surprise victors after a magnificent defensive display. On Sunday, however, they were simply a better all-round team who earned a victory that may yet prove to be a statement of intent that they are genuine contenders for the Six Nations crown.