Vonn was chasing a record-equalling 62nd career win after winning Saturday's downhill in the FIS Alpine Ski World Cup.
The American was .01 seconds ahead of Goergl's time on the first split, only to slide off course when going too tightly into a turn.
Her fall left spectators concerned, but Vonn got back up without any apparent damage to her troublesome left knee.
Vonn's slip paved the way for Goergl to claim victory, finishing .05 secs ahead of compatriot Anna Fenninger with a time of one minute 25.42 secs in France.
That left her second in the overall super-G standings, 28 points adrift of overall leader Lara Gut - who finished fourth on Sunday.
Slovenia's Tina Maze sits a place further back following her third-placed finish, while Anna Fenninger is fourth.
Vonn, who had been chasing a fourth successive podium, is joint-fifth alongside fellow American Julia Mancuso.