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The Swede was the only non-Canadian skier in the women's final but dramatically claimed gold by pipping Courtney Hoffos in a photo finish.
It was just Hoffos' third World Cup start but she had to settle for silver, with compatriot India Sherret winning bronze and Marielle Thompson coming fourth.
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Last year's World Cup winner Fanny Smith was surprisingly knocked out in her semi-final but the Swiss responded to win the small final and claim fifth place overall.
In the men's event, Kevin Drury avenged his compatriots' defeat by skiing to victory in a nip-and-tuck final.
The Canadian edged past home favourite Youri Duplessis Kergomard to take the win when the Frenchman clipped one of the final flags.
The silver medal Duplessis Kergomard earned was still an impressive return for the 23-year-old from Méribel, who had never even been in the top 32 of a World Cup event before this performance.
Swiss skier Ryan Regez took bronze, while another Frenchman – Jean Frederic Chapuis – came fourth and Jonathan Midol won the small final.
The second event of the ski cross World Cup season takes place in the same location on Saturday.
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