The victory was Svahn's second World Cup victory of the season and the 18th overall in her career.
Only Gunde Svan, with 30, and Stina Nilsson, with 22, have more World Cup victories in Swedish skiing history, according to Viaplay.
"It's so great to compete here in Falun. It was my second freestyle here today. I was looking forward to it. A good day," said Svahn in Viaplay's broadcast.
“Gives us luck”
It was a duel for victory when Linn Svahn and Norwegian Kristine Stavås Skistad reached the run-up in front of, among others, King Carl Gustaf, who, just like during the Olympics in Italy, traveled to follow the Swedish national ski team.
"It's nice, we have to prove ourselves when he's here watching. It feels like he brings luck to the team, hopefully he continues to follow us," said Svahn.
The women's final featured three Swedes. Maja Dahlqvist came fifth and Johanna Hagström finished sixth and last in the final.
108th victory for the Olympic king
Emma Ribom advanced to the quarterfinals from the qualifiers but chose to drop out of further competition.
Jonna Sundling, silver medalist in the Olympic sprint and gold medalist in the sprint relay, was ill and was not present.
On the men's side, unsurprisingly, Norwegian Olympic champion Johannes Høsflot Klæbo won easily ahead of compatriot Lars Heggen and Benjamin Moser from Austria.
The victory was the 108th World Cup victory of Klæbo's career; he took six out of six possible gold medals during the Olympics in Italy.
The best Swedes of the day were George Ersson and Anton Grahn, who were both eliminated in the semifinals.
