The Italian, who has never won a major race before, came home in a time of one minute 13.59 seconds, beating Janica Kostelic by 0.05 seconds.
Ceccarelli's compatriot Karen Putzer finished in third on the Wildflower course.
Few pre-race favourites in the alpine skiing events have lived up to their billing at the Games, and Ceccarelli ensured that that trend kept going.
The 26-year-old had shown signs of her potential in the build-up to the Olympics with her first two World Cup podium finishes.
Starting ninth, she put together an incredible run to take pole position from Putzer, before waiting in the finishing area to see if any of her peers could better it.
She threw caution to the wind, carving through the turns with speed, and built up momentum with a direct jump in the middle section that carried her through to the line.
Kostelic came close to adding to her combined gold, but that run apart, Ceccarelli enjoyed a largely comfortable wait.
"I knew I could pull out a good run on this piste as it's fairly long, which is as I like it. It was a bit like St. Moritz," Ceccarelli said.
"I thought for a moment I was only ninth when I got to the bottom as I saw the number flash up. But it was my bib number!
Putzer had set her target early, and it proved too much for either of the pre-race favourites, Renate Goetschl and Hilde Gerg.
Gerg was followed by Ceccarelli, and, barring Kostelic, none of the later starters could get close to even claiming a place on the podium
As the sun climbed in the sky, the top of the course softened and in turn broke the hopes of numerous skiers.
Home favourite Caroline Lalive fell to complete a terrible major record statistic - eight starts and eight falls.
The American was the first of a trio of crashes, Austria's Tanja Schneider and Switzerland's Sylviane Berthod completing the triumvirate.
Germany's Martina Ertl attacked the course after enduring a long wait in the starting gate following Berthod's recovery from the course netting.
However, the mistakes took their toll and the German finished down the pecking order.
Janette Hargin of Sweden also failed to make much of an impression, and in the very next run, when Germany's Regina Haeusl crashed out, Ceccarelli's gold was confirmed.
Britain's Chemmy Alcott, a late starter, finished in 28th.