The 33-year-old Fill mastered the daunting Streif course best on a difficult day with reduced visibility, rolling with the bumps in a smooth run as others struggled to hang on.
Organisers eventually decided to stop the event after the first 30 had raced, citing safety concerns. Six of the 30 did not finish and 27 did not start.
Swiss Beat Feuz was second, 0.37 seconds behind the Italian with fellow Swiss Carlo Janka in third place.
Norwegian Svindal, the pre-race favourite, who had won the men's super G on Friday, was on track to take the lead from Fill when he landed badly from the Hausbergkante jump midway down the course and slid into the protective side netting, leaving the course with a bloody nose.
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He was later ruled out for the rest of the season after undergoing surgery in Innsbruck.
"Detailed checking in Innsbruck showed that the overall World Cup leader torn (sic) his right knee's ACL and underwent surgery in Innsbruck on Saturday," the international skiing federation said. "Svindal will be out for the rest of the season."
Snowfall and strong winds had delayed the competition by about an hour with organisers shortening the start of the Streif course, arguably the most demanding on the World Cup calendar, to reduce speed amid limited visibility.
Apart from Svindal, the course claimed several more skiers, including local favourites Hannes Reichelt and Georg Streitberger, who both needed to be airlifted off the course after crashing out at the same spot as the Norwegian.
Streitberger also suffered a season-ending cruciate ligament tear while Reichelt will be out for two to three weeks.
"It does not seem to be as cold as before and the course may not be as icy so skis sink a bit deeper," said winner Fill. "It is a dangerous course. Very demanding."
(Reporting by Karolos Grohmann; editing by Ken Ferris and Pritha Sarkar)
