Falla finished in 2min 35.49sec, just 0.38sec in front of fellow Norwegian Ingvild Flugstad Oestberg. Slovenian Vesna Fabjan (2:35.89) won bronze.
Norway's Astrid Uhrenholdt Jacobsen, competing despite the death of her brother last week, finished fourth.
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In a stark demonstration of the strength in depth of the Norwegian team, Nordic superstar Marit Bjørgen, who won the skiathlon at the weekend, did not qualify for the final.