Schwarz injured as Sarrazin takes Bormio downhill
Schwarz came into the event with an eight-point lead over Marco Odermatt in the overall standings but he appeared to twist his right knee as he ended up in the safety nets halfway down the course.
The 28-year-old Austrian, who won the slalom at Madonna di Campiglio last week, did not move for several minutes but after some help from paramedics, he was able to limp away without support.
He was later airlifted by helicopter to hospital.
Odermatt, the two-time title holder, subsequently took over top spot in the standings as he finished 0.09 seconds behind Sarrazin. The Canadian Cameron Alexander was third, 1.23 seconds behind the winner.
Odermatt is 72 points clear of Schwarz whose place in Friday's super-G is now in doubt.
It marked just a second World Cup win for the 29-year-old Sarrazin whose only other victory came in his seventh race -- the parallel giant slalom at Alta Badia in December 2016.
But he has been in good form latterly, finishing fourth in the second downhill at Val Gardena a fortnight ago, and pushed to the limit with some risky skiing on the demanding Stelvio piste.
He is the first French skier to win a World Cup downhill since Adrien Theaux won in Santa Caterina in December 2015.
"I finally put together a perfect race," Sarrazin told Eurosport.
"When I crossed the line I said to myself 'you did your job'."