The 29-year-old, whose only other World Cup success came nearly ten years ago at Lake Louise, timed 1 minute 9.53 seconds on the Olimpia delle Tofane piste with Canadian Larisa Yurkiw second 00.15secs slower, and Viktoria Rebensburg of Germany at 00.31secs.
American speed queen Lindsey Vonn, who had been out to get a record-equalling 62nd World Cup win, level with Austrian Anne-Marie Moser-Proell, could only place tenth in a time that was 00.88secs off the pace.
She will have two other chances to equal the record at Cortina over the weekend with a second downhill on Saturday and a super-G on Sunday.
Vonn, who came back from knee surgery to win back-to-back races at the start of the World Cup season, was unable to use her power over a course that was shortened by around 30 seconds due to fog up near the start.
"It just wasn't my day," said the 30-year-old American four-time World Cup winner. "It can only get better."
Vonn had been fastest in training on Thursday but she was not the only one of the favourites to find the going hard.
World Cup leader Tina Maze of Slovenia could only manage 13th place, while Austria's Anna Fenniger was fifth.
There was no such problems for Fanchini who said the previous evening she had watched a video of fellow Italian Isolde Kistner winning at Cortina in 2001.
"She was the last Italian to win a downhill at Cortina and I just tried to do the same as her.
"I have had so many injuries during my career. My knees and my shoulders are always painful but I am so passionate about skiing that I have never even considered stopping."
Despite having an off-day, Maze still managed to increase her lead atop the overall rankings. She currently has 877 points, 272 points ahead of second-placed, Mikaela Shiffrin of the United States.