Schiavone, who before this week had never been beyond the last eight of a major, tamed Stosur's greater power to win 6-4, 7-6. She completed victory after one hour and 38 minutes when Stosur's mishit backhand flew into the crowd.
Both women were making their grand slam final debuts but it was the 29-year-old Schiavone who seized her chance, hustling and harrying Stosur with some tremendous attacking tennis.
After dropping the first set Stosur moved 4-1 ahead in the second but the tenacious Schiavone stormed back to take the set into a tiebreak and moved 6-2 ahead with a superb drop volley.
Taking deep breaths to control her excitement, Schiavone needed only one match point to become Italy's first grand slam champion since Adriano Panatta won the men's singles here in 1976. She is also the oldest woman to win her first Grand Slam title since Ann Jones won Wimbledon in 1969.
As the realisation of her achievement hit home she collapsed on to her back before kissing the Court Philippe Chatrier Court surface and then climbing into the stands where she was swallowed in the embraces of her entourage.
"I haven't prepared anything because when I prepare things they never happen," an emotional Schiavone told the crowd as she collected the trophy from former French Open champion Mary Pierce.
"But I felt amazing today, I (felt) like a champion. I am really, really happy. Thank you everybody," she added.
With temperatures approaching 30 degrees Celsius, Stosur began well, holding her first two service games to love but Schiavone was equally solid behind her own serve, mixing up her groundstrokes to good effect.
The variety of the Italian's game meant Stosur, 26, was unable to get her feet set to unleash the forehand that had helped her to victories over four-times champion Justine Henin, world number one Serena Williams and Jelena Jankovic.
Stosur battled to hold serve from 0-30 in the fifth game, while Schiavone had to fight hard to hold off the Australian in the next game, although she did not face break point.
The next two games went with serve but at 4-4, two poor mistakes from Stosur and then a bold approach from the Italian handed her three break points.
Stosur saved the first two, the second with the help of a fortunate net cord, but then sent down her first double fault to hand the Italian the chance to serve out the set.
A brilliant backhand return helped Stosur save the first set point but two points later she dumped a nervy backhand in the net to give Schiavone the advantage.
Stosur saved two break points and hold serve in the third game of the second set and then finally broke the Italian's serve to move into a 4-1 lead as the cries of "Aussie, Aussie, Aussie" rung out from some of the Australians in the crowd.
Schiavone held serve in the next game to get her teeth back into the set and Stosur faltered again, firing an easy forehand wide to put her opponent back on serve at 3-4.
Both players were making more mistakes than usual at that stage but neither threatened the other on serve and a tiebreak was almost inevitable.
The first four points went with serve but Schiavone got the first mini-break with a backhand pass to lead 3-2 and from there she never looked back.
A superb angled backhand volley gave her match point and when Stosur framed a backhand into the stands the celebrations could begin in earnest.
Pre-match favourite Stosur, struggling to hold back the tears, was gracious in defeat as she missed out on becoming the first Australian woman to win a grand slam singles title since Evonne Goolagong at Wimbldon in 1980.
"First of all, Franc, well done," the Australian seventh seed, said.
"You played very well today, you had a great tournament and good luck for the rest of the year," she added.
She also thanked her mum, dad and two brothers who had flown halfway around the world to watch the biggest day of her career.