Lindell-Vikarby turned in a combined two-run time of 2 minutes, 17.92 seconds and claimed her first World Cup victory by a mere 0.09 seconds over Mikaela Shiffrin of the United States.
Tina Weirather of Lichtenstein took third and another Swede, Maria Pietilae-Holmner edged out Germany's Maria Hofl-Riesch for fourth place.
Lindell-Vikarby, who placed eighth in the season's first giant slalom at Solden, took a wide lead in the first run with a time of 1:06.69 and said the excellent snow conditions allowed her to hold off Shiffrin and the hard-charging Weirather.
"Being in the lead after the first run was something new to me," Lindell-Vikarby said. "I was for sure nervous, but tried to relax, breathe and stay calm. Conditions today were perfect, I couldn't even tell that 29 racers ran before me."