Hector finished 1.17 seconds behind winner Alice Robinson from New Zealand. Julia Scheib from Austria finished second, and Norway's Thea Louise Stjernesund took third place after being the best of everyone in the second run.
Stjernesund was only nine hundredths faster than Sara Hector, who was chasing her eighth victory in the World Cup.
Last season, Hector took four podiums in giant slalom, two of which were victories. He also took two podiums in slalom.
In the giant slalom premiere in Sölden at the end of October, Hector finished ninth.
The other Swedes Estelle Alphand and Hanna Aronsson Elfman finished in 20th and 21st place respectively, 2.64 and 2.69 seconds behind Alice Robinson.
American superstar Mikaela Shiffrin ended up in 14th place after two mediocre runs.
On Sunday, new chances await the Swedes when slalom awaits in Copper Mountain, starting at 6:00 PM.
